630.7 
I26b 
no. 165 
cop.  8 


•^ 


UNIVERSITY  OF 

ILLINOIS  LIBRARY 

AT  URBANA-CHAMPAIGN 

AGRICULTURE 


Rl 


L  t - 


CIRCULATING  C 


Contents  of  Bulletin  No.    165 

PART  I.    THE  STATISTICAL  INTERPRETATION  OF  FEEDING 

EXPERIMENTS 

1.  Introduction. — Value  of  feeding  experiments.  Difficulties  of  interpre- 
tation. Factors  producing  gains  in  weight.  The  problem  to  be  studied.  Gen- 
eral method  of  solution Pages  4G3  to  4G7 

2.  The  Frequency  Distribution  and  the  Average. — The  frequency  distri- 
bution. The  normal  frequency  curve.  The  average  as  a  type.  The  average  as 
a  descriptive   value. Pages  467  to  472 

3.  Variation  and  its  Measurement. — Th?  range  of  observations.  The 
standard   deviation Pages  472  to  473 

4.  The  Significance  of  an  Aver.\ge  and  its  Probable  Error. — The  stand- 
ard deviation  of  an  average.  The  frequency  distribution  of  an  average.  The 
probable  error  of  an  average.    The  limits  of  practical  certainty. Pages  473  to  478 

5.  Illustrations  of  the  Use  of  the  Probable  Error.         Pages  478  to  480 

6.  A  Probability  Method  for  Small  Lots  of  Animals Page  480 

PART  II.    A  STATISTICAL  STUDY  OF  VARIATION  IN  THE  GAINS 
IN  WEIGHT  OF  FARM  ANIMALS  UNDER  LIKE  CONDITIONS 

7.  Introduction. — ^J.  B.  Lawes  on  variation.  The  coefficient  of  variation. 
Pages  481  to  483 

8.  Coefficients  of  Variation  Ordinarily  Obtained  in  Feeding  Experi- 
ments.— Results  of  Wood  and  Stratton.  Results  of  Robinson  and  Hainan.  Re- 
sults obtained  from  American  experiments.  Results  obtained  at  Woburn  and 
Rothamsted.  Discrepancies  among  coefficients.  Meaning  of  such  discrepancies. 
Pages   483    to   487 

9.  Number  of  Animals  per  Lot  Required  in  Feeding  Experiments. — Ad- 
vantages of  large  lots  of  animals Pages  487  to  489 

10.  Size   of   Gains   and   Their   Variability. — Evidence    for   sheep,    swine, 
steers,  and  poultry.     Summary  of  evidence Pages  490  to  492 

11.  Reduction  of  the  Experimental  Error  in  Feeding  Experiments. 

(a)  Importance  of  reducing  the  experimental  error..  .Pages  493  to  496 

(b)  Selection  of  animals  as  regards  age,  breed,  sex,  and  previous 
treatment.     Conclusion Pages  496  to  507 

(c)  Changes  in  variability  of  gains  during  the  course  of  a  feeding  ex- 
periment. Rothamsted  experiments  with  sheep.  Woburn  experiments 
with  sheep.  Iowa  experiment  with  pigs.  Michigan  experiment  with  pigs. 
Illinois  experiment  with  steers.     Canadian  experiment  with  steers.     Sum- 

.     mary  of  evidence Pages  507  to  512 

(d)  Effect  of  change  of  ration  on  variability  of  gains.  Illinois  ex- 
periment with  sheep.  Wisconsin  experiments  with  swine.  Henry's  experi- 
ments at  Wisconsin  with  pigs.  Wisconsin  experiment  with  lambs.  Penn- 
sylvania experiments  with  steers.  Woburn  experiment  with  sheep.  Con- 
clusions  Pages  512  to  526 

(e)  Physiological  selection  of  animals  for  feeding  experiments.  Theo- 
retical considerations.  Does  physiological  selection  eliminate  poor  gain- 
ers? Does  physiological  selection  reduce  the  experimental  error?  Con- 
clusions   Pages  526  to  534 

(f )  Summary  of  methods  of  reducing  experimental  error 

-  • rages  534  to  535 


12.  Repetition  of  Feeding  Experiments. — Henry's  experiments  at  Wisconsin 
with  pigs.  Wyoming  experiments  with  sheep.  Montana  experiments  with 
sheep.  Minnesota  and  Pennsylvania  experiments  with  steers.  Difficulties  of 
repetition.     Probable  explanation   of  these  difficulties Pages  535  to  540 

13.  Variability  in  the  Composition  of  Feedstuffs. — Corn.    Wheat.    Grains 

in  general.     Roughages.     Commercial  concentrates.     Conclusions 

Pages  540  to  548 

PART  III.     SUMMARY  AND  CONCLUSIONS 

APPENDIX 

14.  Statistical  Data  Concerning  the  Rate  of  Growth  of  Sheep,  Swine, 
Steers,  and  Poultry Pages  558  to  570 

15.  Number  of  Animals  to  Include  in  an  Experimental  Lot,  Derivation 
of  Formula Pages  571  to  572 

16.  Change  in  Variability  of  Gains  in  Weight  as  Related  to  Feed  Con- 
sumption.     (Additional   Data.)    Pages  573  to  577 

17.  Bibliography Pages  578   to   579 


■A 


THE  ELEMENT  OF  UNCERTAINTY  IN  THE 

INTERPRETATION  OF  FEEDING 

EXPERIMENTS 

By  H.  H.  MITCHELL,  Assistant  Chemist,  and 
H.  S.  GRINDLEY,  Chief  in  Animai.  Chemistry 

PART  I.     THE  STATISTICAL  INTERPRETATION  OF 
FEEDING  EXPERIMENTS 

Introduction 

Value  of  Feeding  Experiments. — The  purpose  of  the  type  of 
feeding  experiment  considered  in  this  bulletin  is  the  comparison 
of  the  fattening  value  of  two  or  more  systems  of  treatment 
of  farm  animals  or  of  the  fattening  qualities  of  two  or  more 
groups  of  animals  differing  in  age,  breed,  type,  condition,  or  other 
particular.  This  comparison  is  made  on  the  basis  of  the  gains  in 
weight  recorded,  the  feed  consumption,  the  results  of  the  block 
test,  and  the  economic  considerations  involved.  Such  an  experi- 
ment is  the  most  direct  means  of  attacking  many  of  the  problems 
confronting  the  live-stock  farmer.  Our  knowledge  of  the  prin- 
ciples of  animal  nutrition  is  too  fragmentary  to  enable  us  to  fore- 
tell with  certainty,  except  when  greatly  dissimilar,  which  of  two 
rations,  for  instance,  will  produce  the  more  rapid  or  the  more 
economical  gains  in  weight  for  a  particular  kind  of  farm  animal, 
no  matter  how  clearly  defined  or  completely  analyzed  the  rations 
may  be.  Actual  experiment  with  those  particular  rations  is  gen- 
erally essential  to  a  satisfactory  solution  of  the  problem.  How- 
ever, the  information  thus  obtained  has  at  best  a  very  limited  ap- 
plication to  other  rations  or  other  conditions,  so  that  such  feeding 
experiments  ordinarily  contribute  little  of  fundamental  importance 
to  the  science  of  animal  nutrition. 

Difficulties  of  Interpretation. — The  plan  of  the  ordinary  feed- 
ing experiment,  such  as  defined  in  the  preceding  paragraph,  is 
simple,  but  when  completed  its  results  are  often  of  ambiguous  sig- 
nificance, '^nd  the  problem  of  their  rational  interpretation  is  in 
any  case  worthy  of  the  most  careful  attention.  This  is  peculiarly 
tru  oi  experiment  station  work,  upon  which  recommendations  to 
the  farming  community  are  made.     The  difficulty  of  interpreting 

463 


464  Bulletin  Xo.  1G.>  [July, 

the  results  of  the  feeding  experiment  may  be  diminished  to  a  con- 
siderable extent  by  taking  great  care  in  the  selection  of  experi- 
mental animals  and  by  controlling  experimental  conditions  as 
carefully  as  possible  or  practicable;  but  even  after  such  precautions 
have  been  taken,  a  certain  degree  of  ambiguity  still  attaches  to  the 
experimental  results. 

The  ambiguity  inherent  in  feeding  experiments,  and  in  fact  in 
all  experiments  concerned  with  the  functional  activity  of  living  or- 
ganisms, is  due  to  the  impossibility  of  foretelling  with  certainty 
the  precise  result  that  would  be  obtained  if  the  experiment  were 
repeated  as  carefully  as  possible  upon  other  similar  animals  or 
even  upon  the  same  lots  of  animals.  This  element  of  uncertainty 
in  the  interpretation  of  feeding  trials  is  the  more  pronounced,  of 
course,  when  attention  is  directed  to  the  results  that  would  be 
obtained  by  the  practical  farmer  in  following  the  recommenda- 
tions of  the  experimentalist  based  upon  an  investigation  conducted 
by  the  latter,  because  of  the  fact  that  the  farmer  in  many  cases 
cannot  impose  the  precise  experimental  conditions  required.  Thus, 
an  experiment  station  must  be  doubly  cautious  in  advising  its  farm- 
ing community  as  to  the  systems  of  feeding  that  are  best  to  em- 
])loy,  since,  with  the  most  careful  attention  to  details,  a  greater  or 
less  degree  of  uncertainty  always  exists  as  to  whether  essentially 
the  same  result  would  appear  on  repetition  of  the  experiment. 
Furthermore,  this  uncertainty  is  always  enhanced  by  the  certaintv 
that  the  farming  community  in  general  often  cannot  in  practice 
follow  instructions  to  the  letter. 

The  publication  of  the  results  of  a  feeding  experiment  may  be 
confined  to  a  description  of  the  experimental  animals,  the  rations 
fed,  and  all  other  experimental  conditions,  and  to  a  statem.ent  of 
the  gains  in  live  weight  detained,  the  changes  in  condition  of  the 
animals,  the  financial  gains  or  losses,  etc.  "Such  a  statement  is 
in  itself  valuable  and  not  void  of  interest  because  it  contains  the 
description  of  a  fact,  but  as  long  as  this  fact  is  not  connected  with 
other  facts  its  statement  is  not  so  much  knowledge  as  the  material 
for  the  future  acquisition  of  knowledge.  On  this  ground  one  even 
cannot  conclude  that  under  similar  conditions  results  will  be  ob- 
tained which  resemble  those  of  the  first  series  of  observations.  It 
is,  indeed,  out  of  the  question  to  reproduce  exactly  the  same  con- 
ditions, and,  since  one  does  not  know  anything  about  the  conditions 
which  necessitate  the  result,  one  cannot  positively  say  that  only 
the  observed  conditions  are  of  importance  and  one  n  'ist  resign 
the  hope  to  foretell  future  results.  But  the  main  interest  of  all 
investigations  is  to  know  whether  the  same,  or  at  least  sneillar 
results  will  be  obtained  in  a  future  repetition  of  the  observation. 
Before  such  a  statement  can  be  made  it  is  necessary  to  forni  one's 


I 


/pij]  Uncertainty  in  Interpretation  of  Feeding  Experiments  465 

views  about  the  causes  which  were  at  work  to  produce  the  first 
result."^ 

Factors  Producing  Gains  in  Weight. — In  deahng  with  experi- 
mental observations  on  hving  org'anisms,  such  as  observations  on 
rates  of  gain  in  Hve  weight  of  farm  animals,  one  forms  the  hy- 
pothesis that  the  experimental  results,  i.  e.,  the  gains  in  weight 
actually  obtained,  are  due,  in  the  first  place,  to  a  complex  of  con- 
ditions definitely  imposed  upon  the  subjects  of  the  experiment  and 
under  relatively  perfect  control.  These  conditions  consist,  for  in- 
stance, of  the  rations  fed,  the  preparation  of  the  rations,  the 
method  and  times  of  feeding,  the  method  of  sheltering,  weighing, 
and  exercising  the  animals,  the  season  in  which  the  experiment  is 
run,  etc.  If  the  feeding  experiment  be  repeated,  it  is  this  com- 
plex of  conditions  that  it  is  possible  to  maintain  constant.  In  the 
second  place,  the  gains  in  weight  obtained  must  be  considered  as 
being  influenced  also  by  another  group  of  conditions  not  under 
control.  These  conditions  may  be  considered  as  consisting  of  the 
temperaments  of  the  animals  as  evidenced  in  their  differential  physi- 
cal activity,  their  feeding  capacities,  their  physiological  peculiari- 
ties, and  all  of  the  functional  characteristics  that  render  one  animal 
distinct  from  another  and  are  known  collectively  as  its  individuality . 
Besides  the  individualities  of  the  experimental  animals,  there  must 
be  included  in  this  second  group  of  causal  conditions  the  environ- 
mental conditions  not  under  control,  such  as  the  weather,  and  even 
the  personality  of  the  attendant.  Such  uncontrolled  conditions  can- 
not be  kept  constant,  of  course,  from  one  experiment  to  another, 
but  are  necessarily  variable.  Therefore,  they  constitute  the  ele- 
ment of  uncertainty  in  the  full  interpretation  of  the  results  of 
feeding  experiments.  In  (^rder  to  deal  with  these  variable  condi- 
tions in  foretelling  the  result  of  repeating  such  an  experiment,  we 
merely  assume  that  their  influence  on  the  rate  of  gain  in  live  weight 
is  perfectly  random,  showing  no  recognizable  law  or  regularity  ex- 
cept in  a  large  series  of  observations.  As  Urban  aptly  says,  "We 
base  our  expectation  that  a  repetition  of  the  series  of  experiments 
will  give  similar  results  on  the  identity  of  the  conditions  which 
we  know  and  on  the  supposition  of  the  random  character  of  the 
influences  which  we  do  not  know." 

The  Problem  to  be  Studied. — It  is  the  purpose  of  this  sec- 
tion of  the  bulletin  to  consider  the  element  of  uncertainty  in  the 
interpretation  of  the  results  of  feeding  experiments  due  to  these 
variable,  uncontrolled,  and  largely  unknown  experimental  condi- 
tions, and  to  propose  methods  of  dealing  with  the  question  in  a 
systematic  and  rational  manner,  so  that  the  sphere  of  uncertainty 

'F.  M.  Urban,  Exp.  Stud,  in  Psych,  and  Ped.,  Ill,  "The  Application  of  Sta- 
tistical Methods  to  the  Problems  of  Psychophysics,"  p.  19.     Phila.,  1908. 


466  Bulletin  No.  165  [/»^y, 

surrounding  the  conclusions  based  on  experimental  results  will 
be  reduced  to  a  minimum  and  be  defined  as  clearly  as  possible. 
The  methods  proposed  have  been  employed  in  other  and  closely 
related  fields  of  research  and,  in  fact,  have  already  been  applied 
in  a  brief  manner  to  one  of  the  many  problems  connected  with  feed- 
ing- experiments,  by  Wood  and  Stratton,^  and  later  by  Robinson 
and  Hainan,''  of  Cambridge  University. 

A  feeding  experiment  involves  not  only  a  record  and  interpre- 
tation of  the  feed  consumption  and  the  gains  of  each  lot,  but  also 
a  statement  of  the  cost  of  the  experimental  animals  and  of  the 
feeds  consumed  as  compared  with  a  statement  of  the  price  real- 
ized on  the  animals  of  each  lot  when  sold.  The  question  of  the 
relative  emphasis  to  be  placed  on  these  two  subdivisions  of  the  sub- 
ject matter  of  a  feeding  experiment  is  of  importance.  In  view  of 
the  fact  that  the  feed  consumption  and  the  resulting  gains  of  a 
given  lot  of  animals  on  a  given  ration  determine  the  final  condi- 
tion of  the  animals  and  afford  the  basis  for  the  economic  considera- 
tions involved  in  a  feeding  experiment,  and  in  view  of  the  fact 
that  "conditions  as  to  market  price  of  feeding  and  fat  cattle  and 
cost  of  feeds  have  ne\er  been  identical  during  any  two  consecutive 
years  and  seldom  more  than  similar  at  irregular  intervals,"*^  it  is 
ob\'ious  that  the  most  valuable  data  of  a  feeding  experiment  are 
the  data  concerning  the  feed  consumption  and  the  rapidity  of  gain 
of  the  class  of  farm  animals  from  which  the  experimental  ani- 
mals were  drawn.  B.  E.  Carmichael  takes  substantially  the  same 
position  in  the  following  quotation : 

"The  author  is  thoroughly  convinced  that  too  important  a  place  is  often 
given  to  the  cost  of  gains  when  discussing  the  results  of  a  feeding  experiment, 
thus  rendering  more  probable  a  wrong  understanding  by  the  student  or  feeder. 
When  feeders  and  experimenters  think,  reckon,  and  write  concerning  feeding 
experiments  with  amount  of  feed  and  rate  and  extent  of  gain  in  live  weight, 
rather  than  zcith  cost  cff  feed,  animals,  and  gains  and  net  proUt  from  the  opera- 
tion as  the  factors  for  comparisons,  it  will  be  reasonable  to  expect  more  intel- 
ligent selection  of  rations  and  consequently  fewer  failures  to  secure  satisfactory 
returns  for  feed  and  labor  required  to  conduct  feeding  operations. 

"The  writer  would  not  be  understood  as  saying  that  a  financial  statement 
is  of  no  value  or  that  nothing  should  be  said  concerning  the  cost  of  gains.  On 
the  contrary,  each  has  a  value,  but  it  is  believed  that  in  either  case  the  value  is 
far  less  important  than  is  the  matter  of  the  amount  of  feed  required  to  produce 
a  given  gain,  on  account  of  the  sudden  and  wide  variation  in  price  that  may 
occur."" 

The  feed  consumption  in  feeding  experiments,  according  to 
the  ordinary  practice,  is  determined  for  the  entire  lot  rather  than 
for  the  individual  animals,  and  such  total  data  are  not  susceptible 

•Journ.  Agr.  Sci.,  vol.  3,  pp.  417-440.  1908-10.  See  also  T.  B.  Wood,  Journ. 
Board  Agr.,  London,  Sup.  7,  1911,  Nov.,  pp.  32-37. 

"Journ.  Agr.  Sci..  vol.  5,  pp.  48-51.     October,  1912. 
'Herbert  W.  Mumford,  111.  Agr.  Exp.  Sta.,  Bui.  90,  p.  203, 
"Ohio  .Agr.  Exp.  Sta.,  Bui.  187.  pp.  18  and  19. 


^913]  UXCERTAIXTY    IX    IXTERPRETATIOX    OF    FeEDIXG    ExpERIMEXTS  467 

to  treatment  by  the  methods  to  be  outlined  below.  In  this  bulletin, 
therefore,  attention  is  conhned  to  the  gains  in  weights  obtained 
in  feeding  experiments  and  to  the  methods  of  comparing  ade- 
quately the  gains  of  two  or  more  lots  of  animals,  since  in  many 
experiments  individual  gains  are  reported. 

General  Method  of  Solution. — The  problem  of  the  feeding  ex- 
periment that  is  considered  in  this  section  of  the  bulletin  is 
the  comparison  of  a  number  of  gains  in  weight  made  by  animals 
in  one  lot,  treated  alike  as  far  as  practicable,  with  a  number  of 
gains  in  weight  made  by  animals  in  another  lot,  treated  alike,  but 
in  one  particular  treated  differently  from  the  animals  of  the  first 
lot,  the  object  of  the  comparison  being  to  determine  whether  the 
one  difference  in  treatment  between  the  two  lots  has  produced  a 
dift'erence  in  the  rate  of  gain  in  weight.  This  comparison  may  be 
most  effectually  made  by  considering  the  two  series  of  gains  sepa- 
rately at  first,  with  the  idea  of  describing  each  adequately,  but 
with  as  few  terms  as  possible,  and  then  comparing  the  two  ab- 
breviated descriptions. 

The  Frequexcy  Distributiox  and  the  Average^ 

In  describing  the  gains  made  by  a  group  of  animals,  the  total 
gain  of  the  group  is  often  taken,  but  for  comparative  purposes  it 
is  almost  universallv  considered  that  it  is  better  to  reduce  this 
total  gain  to  a  per  capita  basis,  and  hence  it  is  generally  the  case 
that  the  common  average  or  arithmetic  mean  of  the  individual 
gains  of  a  lot  is  the  one  value  taken  as  descriptive  of  the  lot. 

When  a  chemist  runs  a  series  of  atomic  W' eight  determinations 
upon  a  chemical  element,  and  subsequently  takes  the  average  of 
his  results,  this  average  has  a  perfectly  definite  physical  signifi- 
cance, f.  e.^  it  is  the  best  approximation  obtainable  to  the  actual 
atomic  weight  of  the  element.  However,  the  case  is  quite  different 
when  the  investigator  in  animal  nutrition  averages  the  gains  in 
weight  made  by  a  group  of  similarly  treated  animals  during  the 
same  period  of  time.  Strictly  speaking,  there  is  nothing  here  that 
can  be  called  a  "true  value"  to  be  obtained  from  a  set  of  values 
diverging  from  it  as  the  result  of  errors  of  observation.  The 
distinction  between  the  two  cases  is  well  brought  out  by  Edgeworth 
when  he  says  that  observations,  such  as  those  of  the  chemist,  "are 
different  copies  of  the  same  original,"  while  statistics,  such  as 
those  of  gains  in  wei^lit  of  a  lot  of  animals,  "are  different  origi- 
nals affording  one  generic  portrait." 

The  meaning  of  the  average  of  a  set  of  statistics  may  be  con- 
sidered in  the  following  way :    It  is  conceivable  that  the  aggregate 


'In  the  following  discussion,  "average"  refers  to  the  arithmetic  mean. 


I 


468  Bulletin  No.   165  [July, 

of  the  direct ly  imposed  experimental  conditions  under  which  the 
gains  in  weight  were  made,  operated  in  the  production  of  a  typical 
gain,  from  which  the  individual  gains  diverge  as  the  result  of  the 
casual  or  random  sources  of  variation,  and  the  average  gain  may 
be  considered  as  the  best  approximation  to  this  type. 

The  Frequency  Distribution. — In  considering  this  conception  of 
the  average  gain  in  w-eight  of  farm  animals  treated  in  a  similar 
manner,  it  is  necessary  to  investigate  the  frequency  distribution  of 
such  gains.  Suppose  a  large  number  of  animals,  say  several  hun- 
dred, were  treated  alike  as  far  as  possible  with  regard  to  feed, 
shelter,  etc.,  and  suppose  the  average  daily  gain  in  weight  for  each 
animal  be  determined  for  a  considerable  period  of  time,  say  one 
hundred  days.  Suppose  the  daily  gains  thus  obtained  be  grouped 
into  class  intervals  of  o.  i  lb.  and  the  number  of  gains  occurring 
within  each  class  interval  be  noted.  The  series  of  numbers  thus 
obtained  is  known  as  a  frequency  distribution,  since  it  gives  the 
frequency  with  which  gains  of  any  given  magnitude  occur.  There 
are,  of  course,  no  data  in  existence  of  the  gains  in  weight  made  by 
several  hundred  animals  treated  alike  at  the  same  place  and  during 
the  same  time.  Therefore,  in  obtaining  such  frequency  distribu- 
tions an  indirect  method  has  been  employed. 

In  obtaining  the  numbers  upon  which  Fig.  i  of  the  chart  is 
based — this  figure  being  a  graphical  representation  of  the  frequency 
distribution  of  the  daily  gains  in  weight  of  498  sheep — the  average 
daily  gains  made  by  46  lots  of  sheep  were  taken,  the  lots  varying 
in  size  from  8  to  16  sheep.  The  lots  were  treated  in  different  ways, 
of  course,  and  at  different  stations  during  different  periods  of  time. 
In  combining  the  dift'erent  gains  for  the  purpose  of  forming  one 
distribution,  it  was  desired  to  eliminate  the  variation  due  to  dif- 
ferences in  feed  and  other  definite  factors,  and  to  retain  only  that 
variation  due  entirely  to  the  casual  factors,  such  as  individuality 
and  imperfectly  controlled  conditions.  In  accomplishing  this  ob- 
ject, the  average  daily  gain  in  weight  of  the  entire  group  of  498 
sheep  was  obtained  and  found  to  he  0.3485  lb.  Xext,  the  gains  in 
each  of  the  46  lots  were  changed,  or  transmuted,  by  addition  or 
subtraction  so  that  the  average  daily  gains  of  the  various  lots 
were  made  identical  and  approximately  equal  to  0.3485  lb.  Thus, 
the  first  lot  so  treated  consisted  of  10  sheep  with  an  average  daily 
gain  of  0.283  lb.  By  adding  to  each  of  the  ten  gains  in  the  lot  the 
difference  between  0.283  lb.  and  0.348  lb.,  which  is  equal  to  0.065 
lb.,  the  desired  change  was  accomplished,  ^or  another  lot  of  ten 
animals  with  an  average  daily  gain  of  0.413  lb.,  0.065  lb.  was  sub- 
tracted from  each  of  the  individual  gains.  Ry  thus  making  the 
average  gains  of  the  46  lots  identical  without  disturbing  the  vari- 
ation within  the  lots,  it  was  believed  that  the  intluence  of  the  dif- 


voiua* 

.10 

.15 

.20 

Z5 

.30 

.35 

40 

4S 

.SO 

.55 

.60 

Tr.- 

3 

7 

27 

44 

92 

129 

121 

48 

21 

5 

1 

.        1 

Class 
value* 

75 

1.00 

1.25 

1.50 

175 

2.00 

Z 

Fr«- 
qu»ncici 

1 

2 

7 

20 

48 

63 

FIG.  I  FIG.  3 

Frec^uency  Distribution  of  the  Daily        Frequency  Distribution  ( 
Gains  in  V/eight  of  498  Shee}^.  Gains  in  Weight  of  241 


1.75 


48 


63 


2.O0I225 


59 


ZZ 


a502.75 


13 


3.00325 


Cltiss 

values 


.60 


.70 


.80 


li 


.90 


14.5 


26 


1.00  1. 10 


57 


sas 


97 


1.20 1.30  1.40 1.50 1.60 


76.5 


45532.5 


1.70 


7.5 


1.80 


2.5 


i.90i2oda 

I    I 


1.3 


FIG.  3  FIG.  5 

ibution  of  the  Dail\(       Frecjuerjcy  Distribution  of  the  Dailv/   Gains  in 
of  241  Steers.  Weight  of  461  Pigs. 


82.15 


84.75 


87.35 


89.95 


92.55 


93.15 


97.75 


FIG.  7 
Frequency  Distribution  of  the  Coefficients    of 
Digestibility  of  the  Protein  of  a  Normal    Mixed 
Diet,  Obtained  from    1153  Observations    on 
23   Men. 


FIG.  8 
Frequency    Distribution  of  the  Dail^   Excretion 
of  Indican    in   the    Urine,  Obtained  from 
814  Observations  on   U  Men. 


jQij]  Uncertainty  ix  iNTERPkETATiox  ok  1'eeuing  Ilxpekimems  469 

ferent  experimental  conditions  among  the  lots  was  eliminated  as 
far  as  possible,  while  the  inlluence  of  the  casual  factors  represented 
by  the  variation  within  the  lots  was  preserved  intact.  The  498  gains 
thus  transmuted  were  used  in  obtaining  Fig.  i. 

In  this  distribution  the  class  interxal  chosen  was  0.05  lb.,  as  is 
indicated  by  the  first  row  of  figures  at  the  base  of  the  diagram. 
The  second  row  of  figures  gives  the  frequencies  of  the  different 
classes.  Thus,  the  number  129  in  the  middle  compartment  indi- 
cates that  129  of  the  498  daily  gains  in  weight  (transmuted  ac- 
cording to  the  alx)ve  scheme)  fell  within  the  interval  0.325  to 
0.375  lb.,  the  number  directly  above,  i.  e.,  0.35,  being  the  mid- 
value  of  this  class.  The  frequency  distribution  represented  by  this 
second  row  of  numbers  is  graphically  illustrated  by  the  superim- 
posed diagram,  which  is  known  as  a  histogram.  Along  the  base 
of  this  histogram,  equal  spaces  are  marked  ofif  representing  the 
equal  class  divisions.  On  each  space  a  rectangle  is  erected,  the 
height  of  which  is  proportional  to  the  frequency  of  the  respective 
class;  or,  preferably,  since  the  gains  must  be  considered  as  being 
continuously  distributed  along  the  base  line  or  scale  and  merely 
summated  at  ecjual,  convenient,  arbitrary  intervals,  the  areas  of  the 
rectangles  should  be  considered  as  representing  frequency.  Figs. 
3  and  5  represent  the  frequency  distributions  of  the  daily  gains  in 
weight  of  241  steers  and  461  pigs,  respectively,  and  have  been  con- 
structed from  transmuted  values  in  the  same  way  as  Fig.  i. 

The  Normal  freqiieuey  Curve. — It  will  be  seen  from  all  three 
distributions  that  the  frequencies  start  at  zero,  rise  rather  regu- 
larly to  a  maximum,  and  decrease  regularly  to  zero  again,  the  rates 
of  increase  and  of  decrease  being  appreciably  similar.  This  is 
well  shown  in  Figs.  2,  4,  and  6.  In  these  figures  a  curve  of  a 
definite  character,  represented  by  a  definite  equation,  and  known 
as  the  )ioriiial  frequeticy  curie,  has  been  fitted  to  the  three  distribu- 
tions. The  base  lines  of  these  figures  have  been  divided  into  the 
same  equal  divisions  representing  the  same  classes  as  the  figures 
directly  above.  The  closeness  of  the  fit  is  indicated  graphically 
by  the  circled  points  placed  at  distances  above  the  centers  of  the 
class  intervals  proportionate  to  their  actual  frequencies  as  given 
in  the  figures  immediately  above,  and  numerically  by  the  frequency 
values  given  in  the  second  row  of  figures  below.  These  frequency 
values  give  areas  beneath  the  curve  between  ordinates  erected  at 
the  class  limits.  Thus,  the  value  122.7  ^^i  the  second  row  below 
the  center  of  Fig.  2  gives  the  area  bounded  by  the  curve,  the  base 
line,  and  the  ordinates  erected  at  0.325  and  0.375  ^^^-  "'"•  the  hori- 
zontal scale,  and  corresponds  exactly  to  the  value  129  given  in 
Fig.  I.  The  closeness  of  fit  of  these  three  curves  is  apparently  as 
satisfactorv  as  could  be  desired. 


470  Bulletin  No.  165  [July, 

Perhaps  the  most  important  fact  disclosed  by  these  frequency 
distributions  is  that  variations  in  rate  of  gain  in  weight  due  to  un- 
controlled experimental  conditions,  while  exhibiting  no  regularity 
and  rfo  conformance  to  law  as  regards  frequency  of  occurrence  in 
the  small  experiment,  actually  do  exhibit  a  regularity  in  the  long 
run  and  actually  do  conform  to  a  law  that  may  be  considered  as 
being  approximately  represented  by  the  mathematical  definition 
of  the  frequency  curve  satisfactorily  fitting  the  distribution,  i.  e., 
the  normal  law  of  frequency  in  the  cases  under  discussion.  This 
tendency  of  the  casual  variations  in  gain  in  weight  observed  within 
a  lot  of  similarly  treated  animals  to  exhibit  frequencies  of  occur- 
rence in  the  long  run  in  conformity  to  a  mathematically  defined  law 
is  at  the  basis  of  all  attempts  to  predict  the  results  of  future  repe- 
tition of  feeding  experiments  by  finding  the  probability  that  an 
average  lot  gain  or  the  difference  between  two  average  lot  gains  will 
lie  between  any  assigned  limits.  The  law  defining  the  frequency 
of  occurrence  of  casual  variations  is  simply  a  mathematical  expres- 
sion by  which  the  probability  of  the  occurrence  of  a  given  gain  in 
weight  is  obtained  by  finding  the  extent  of  its  deviation  from  the 
average  gain. 

The  Average  as  a  Type. — Returning  to  the  conception  of  the 
average  gain  in  weight  as  a  type  which  tends  to  be  set  up  by  the 
definite  experimental  conditions  deliberately  imposed,  and  which 
is  only  incompletely  realized  by  reason  of  the  numerous  casual 
factors  which  are  beyond  control,  it  seems  that  in  the  frequency 
distributions  such  a  type  would  be  the  position  on  the  horizontal 
scale  of  the  ordinate  passing  thru  the  summit  of  the  frequency 
curve.  This  is  the  value  of  greatest  frequency,  the  value  more 
often  realized  than  any  other  under  conditions  of  like  control.  In 
Figs.  2,  4,  and  6,  ordinates  are  erected  at  points  on  the  base  lines 
corresponding  to  the  arithmetic  means  of  the  gains  in  weight,  and 
it  will  be  seen  that  the  means  of  the  distributions  may  be  regarded 
as  actually  being  the  points  of  greatest  frequency,  or  at  least  very 
good  approximations  to  such  points. 

From  a  study  of  these  distributions,  it  may  be  considered  that 
a  typical  gain  in  weight  exists  within  the  lot,  and  that  the  aritli- 
metic  mean  of  the  individual  gains  is  as  good  an  approximation 
to  this  t^-pe  as  can  be  readily  obtained.  In  defining  this  typical 
gain  to  which  the  arithmetic  mean  approximates,  we  may  say  that 
it  is  the  gain  that  would  be  realized  by  each  animal  in  the  lot  if 
no  such  thing  as  individuality  existed  and  if  all  experimental  con- 
ditions were  under  complete  control  and  were  kept  constant  for  all 
animals. 

It  may  be  said  in  passing,  however,  that  the  conception  of  the 
arithmetic  mean  as  an  approximation  to  a  type  does  not  apply  to 


/p/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  471 

all  distributions.  Thus,  Fig-.  7  gives  the  frequency  curve  of  the 
coefficients  of  digestibiHty  of  the  protein  of  a  mixed  normal  diet 
from  1 1 53  observations  on  23  men.^"  In  this  case  the  mean  is  dis- 
tinctly situated  to  the  left  of  the  maximum  ordinate,  due  to  the 
peculiar  asymmetry  of  the  curve.  This  condition  may  be  consid- 
ered as  existing  in  all  cases  of  distribution  of  percentages  where 
the  limiting  percent  is  100  and  the  typical  or  modal  percent  is  very 
near  this  limit.  Whatever  considerable  variation  occurs  in  the  per- 
centage, therefore,  must  naturally  draw  out  the  distribution  to  a 
greater  extent  below  the  type,  or,  as  it  is  technically  caWtd,  the  mode, 
than  above  it.  In  Fig.  8  is  shown  another  case  of  asymmetry.  This 
figure  gives  the  frequency  curve  of  the  daily  excretion  of  indican 
in  the  urine,  the  data  for  which  were  obtained  by  Folin  from  814 
observations  on  1 1  men  during  the  course  of  his  experiment  to  de- 
termine the  physiological  effect  of  saccharin.^  Here  the  lower 
physical  limit  of  the  distribution  is,  of  course,  zero,  and  since  the 
typical  value,  or  the  mode,  occurs  near  this  limit,  and  since  the 
variability  is  rather  extreme,  the  distribution  is  drawn  out  above 
the  mode. 

The  Average  as  a  Descriptive  J'aliie. — A  second  conception  of 
the  arithmetic  mean  of  a  series  of  gains  in  weight  made  by  a  lot 
of  uniformly  treated  animals,  is  merely  that  of  a  discriptive  value, 
a  representative  gain  used  in  place  of  the  whole  series  of  gains,  the 
best  representative  perhaps  of  the  series.  Edgeworth  describes  it 
as:  "that  quantity  which,  if  we  must  in  practice  put  one  quantity 
for  many,  minimizes  the  error  unavoidably  attending  such  prac- 
tice."'^ It  must  be  admitted,  however,  that  if  the  best  that  can  be 
said  of  a  mean  is  that  it  is  merely  a  descriptive  value,  it  lacks 
much  that  is  desirable.  It  has  no  physical  meaning  such  as  is  pos- 
sessed by  an  average  that  coincides  with  the  mode.  It  can  be 
defined  only  by  reciting  its  method  of  calculation,  and  not  by  de- 
scribing any  characteristics  that  it  necessarily  possesses.  It  must  be 
regarded  simply  as  the  result  of  a  mathematical  calculation  leading 
to  a  value  occupying  an  intermediate  position  in  the  series,  whose 
principal  claim  to  consideration  is  that  it  is  easily  obtained  and  is 
almost  universally  used,  rightly  or  otherwise.  Furthermore,  the 
calculation  of  the  arithmetic  mean,  leading  as  it  does  to  a  value 
such  that  the  sum  of  the  differences  between  it  and  all  values  below 
it  is  equal  to  the  sum  of  the  differences  between  it  and  all  values 
above  it,  is  most  significant  only  when  the  value  desired  is  the  mid- 
value  of  a  symmetrical  distribution,  and  therefore  where  asym- 
metry distinctly  exists,  the  arithmetic  mean  cannot  but  suffer  a  loss 

"These  data  were  obtained  by  the  Division  of  Animal  Nutrition  of  the  De- 
partment of  Animal  Husbandry  of  this  station. 

"U.  S.  Department  of  Agjriculture,  Report  No.  94.     1911. 
'Edgeworth,  Trans.  Cambridge  Phil.  Soc,  vol.  14. 


472  Bulletin  No.  1G5  [^"0- 

of  significance.  If,  for  instance,  a  chemical  method  of  analysis 
were  such  that  errors  in  defect  of  the  true  value  were  distinctly  and 
decidedly  more  frequent  and  more  important  than  errors  in  excess, 
it  is  evident  that  the  process  of  taking  an  arithmetic  mean  of  a 
number  of  results  obtained  by  such  a  method  would  necessarily  be 
looked  upon  as  leading  more  often  than  not  to  a  result  less  than 
the  desired  value. 

V.VRIATION  AND  ITS  ^^IEASUREMENT 

In  calculating  the  average  gain  exhibited  by  a  lot  of  similarly 
treated  animals,  a  more  or  less  satisfactory  measure  is  obtained 
of  the  influence  of  the  deliberately  imposed  conditions  upon 
the  rate  of  growth.  The  incidental  and  uncontrolled  experimental 
conditions,  constituting  all  individual  and  environmental  factors 
that  have  not  been  kept  constant  thruout  the  lot,  find  direct  and 
complete  expression  in  the  variation,  or  dispersion,  of  the  indi- 
vidual gains.  Hence  a  measure  of  the  variation  of  the  gains  with- 
in the  lot  is  a  measure  of  the  influence  of  the  uncontrolled  factors 
in  the  experiment,  which  always  render  more  or  less  ambiguous 
the  conclusions  ultimately  deduced.  Hence,  also,  such  a  measure 
is  another  value  descriptive  of  a  series  of  gains  in  weight  ob- 
tained under  similar  conditions.  In  fact,  so  far  as  rate  of  growth 
is  concerned,  the  average  lot  gain,  and  a  good  measure  of  the 
variation  of  gains  within  the  lot,  sufficiently  describe  for  all  ordi- 
nary comparative  purposes  the  response  of  the  animals  in  the  lot 
to  the  experimental  conditions. 

In  obtaining  a  measure  of  the  variation  or  the  dispersion  with- 
in the  lot,  it  is  obviously  necessary  to  have  at  hand  the  gains  of  the 
individual  animals.  The  frequent  practice,  in  weighing  up  lots, 
of  obtaining  only  the  total  weight  per  lot,  so  that  only  the  total 
gain  per  lot  for  the  experiment  is  finally  available,  renders  all  study 
of  dispersion  within  the  lots  impossible;  for,  while  the  arithmetic 
mean  of  the  individual  gains  in  weight  is  obtainable  directly  from 
the  total  gain,  any  measure  of  dispersion  must  take  into  considera- 
tion the  individual  gains  and  any  adequate  measure  of  dispersion 
must  take  into  consideration  all  of  the  individual  gains. 

The  Range  of  Observations. — The  simplest  measure  of  disper- 
sion and  the  one  most  commonly  used  is  the  range  of  observations 
actually  obtained,  such  range  being  the  difference  between  the 
minimum  and  the  maximum  values.  However,  it  has  very  little 
to  commend  it,  in  spite  of  its  rather  general  use,  aside  from  the 
ease  of  its  calculation.  Obviously,  one  of  the  properties  of  a  good 
measure  of  dispersion  is  that  it  have  as  high  a  degree  of  staliility 
as  possible  as  we  pass  from  one  lot  of  animals  to  other  and 
other  similarly  treated  lots.  Consider,  for  instance,  a  large  num- 
ber of  lots  of  steers  that  have  been  similarlv  treated  for  the  same 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  473 

period  of  time,  each  lot,  say,  containing  ten  steers.  It  seems  evi- 
dent that  that  measure  of  the  dispersion  of  the  individual  gains  in 
weight  is  best  which  is  the  most  constant  from  lot  to  lot,  since  the 
same  uncontrolled  factors  to  which  are  due  the  variation  within 
the  lots  have  influenced  each  and  every  lot.  But  the  range  from  the 
minimum  to  the  maximum  gain  in  a  lot  is  directly  affected  by  the 
extreme  and  unusual  gains  which  may  have  been  obtained,  the  very 
gains  whose  influence  should  be  minimized  because  of  their  in- 
frequent occurrence  and  non-typical  character.  Furthennore,  sup- 
posing these  lots  of  steers  that  are  under  consideration  are  not  of  the 
same  size,  it  is  evident  that  the  range  of  dispersion  within  the  lots 
will  in  general  increase  with  the  size  of  the  lot,  since  the  steers  ex- 
hibiting extremely  high  or  extremely  low  gains  will  be  found  more 
frequently  in  the  larger  than  in  the  smaller  lots.  Thus,  the  range 
between  the  highest  and  the  lowest  gains  in  a  lot  is  of  little  value 
for  comparative  purposes,  since,  like  the  total  gain,  it  depends  in 
part  upon  the  size  of  the  lot;  but,  unlike  the  total  gain,  the  in- 
fluence of  the  size  of  the  lot  cannot  be  eliminated  by  a  simple 
division  by  the  number  in  the  lot,  or  in  fact,  by  any  other  reason- 
ably simple  mathematical  process 

The  Standard  Dcination. — Obviously,  a  good  measure  of  dis- 
persion must  take  into  consideration  each  and  every  individual 
gain  obtained;  otherwise  it  really  is  not  a  characteristic  of  the 
whole  series  of  gains  and  is  unduly  influenced  by  the  extreme 
gains.  Perhaps  the  first  method  that  occurs  to  one  of  involving 
all  gains  in  a  measure  of  their  dispersion  is  to  take  the  average 
deviation  of  each  of  the  gains  from  their  mean,  paying  no  regard, 
of  course,  to  the  position  of  the  gain — whether  above  or  below 
the  mean.  In  fact,  this  is  an  excellent  measure  of  dispersion  that 
is  sometimes  used  and  is  known  as  the  az'erage  dci'iation.  The 
measure  of  dispersion  in  most  common  use,  however,  is  obtained, 
by  squaring  all  deviations  of  individual  gains  from  the  average, 
adding,  dividing  by  the  number  of  gains,  and  extracting  the  square 
root  of  the  quotient.  This  is  known  as  the  standard  dcination,  or 
the  root-nican-sqnare  deviation  from  the  mean.  While  the  standard 
deviation  is  much  more  difticult  of  calculation,  it  possesses  several 
advantages  over  the  average  deviation,^  and  is  in  more  general  use. 

The  Significance  of  an  Average  and  its  Probable  Error 

The  possession  of  an  adequate  measure  of  variation  at  once 
leads  to  the  problem  of  determining  to  what  extent  variation  with- 

'For  a  very  good  discussion  of  the  average  deviation  and  the  standard  devi- 
ation, see  G.  U.  Yule :  "An  Introduction  to  the  Theory  of  Statistics,"  chap, 
viii.    London :   Chas.  Griffin  &  Co.,  Ltd.    1911. 


474  Bulletin  No.  165  [July, 

m  the  lot  vitiates  conclusions  based  upon  averag-e  lot  gains.  The 
averag-e  lot  gain  and  the  standard  deviation  of  the  individual  gains 
sufficiently  describe  the  lot  for  all  ordinary  comparative  purposes, 
and  the  question  now  at  issue  is  how  these  two  descriptive  terms  can 
be  used  to  render  any  subsequent  comparison  the  most  efficacious. 
As  a  matter  of  fact,  the  average  gain  or  the  total  gain  of  a  similarly 
treated  lot  of  animals  is  a  very  deceptive  quantity  unless  its  exact 
significance  is  quantitatively  defined  by  some  additional  term.  An 
average  gain  should  be  thought  of,  not  so  much  as  an  isolated 
point  in  the  scale  of  measurement,  but  rather  as  the  mid-value  of 
an  interval  such  that  there  is  a  definite  probability  that  upon  repe- 
tition of  the  experiment  the  average  gain  so  obtained  will  fall 
within  it.  Such  an  interval  is  defined  by  the  probable  error  of  the 
average;  and  the  probability  that  repetition  of  the  experiment  will 
yield  an  average  within  the  limits  of  this  probable  error  is  exactly 
one-half.  Raymond  Pearl,  of  the  Maine  Experiment  Station,  who 
is  applying  biometric  methods  to  problems  of  agricultural  science, 
insists  that  "an  experiment  which  takes  no  account  of  the  'prob- 
able error'  of  the  results  reached  is  inadequate  and  as  likely  as 
not  to  lead  to  incorrect  conclusions."* 

Similarly,  \\'ood  and  Stratton  emphasize  strongly  the  advis- 
ability and,  in  fact,  the  necessity  of  allowing  for  errors  of  sampling 
incurred  in  the  selection  of  animals  for  experiment.  The  follow- 
ing quotation  is  especially  significant :  "With  the  great  growth  of 
interest  among  the  farming  community  and  the  increasing  ten- 
dency of  the  farmer  to  take  note  of  the  work  of  the  experimental- 
ist and  to  act  upon  it,  it  is  becoming  increasingly  important  that 
due  caution  should  be  exercised  by  experimenters  in  interpreting 
their  results  before  laying  them  before  the  agricultural  public."'* 

Since  an  attempt  to  allow  for  experimental  error  in  the  inter- 
pretation of  aA-erage  lot  gains  is  not  effective  unless  the  individual 
gains  have  been  obtained,  it  is  obviously  important,  in  conducting 
a  feeding  trial,  to  ascertain  individual  behavior — the  reaction  of 
each  animal  to  the  experimental  conditions  imposed.  Important 
as  this  condition  is,  it  is  too  frequently  disregarded  in  experiment 
station  work.  The  collection  and  publication  of  individual  data 
is  too  often  thought  to  have  little  or  no  bearing  on  the  problem  of 
the  experiment  and  conse(|uently  to  be  a  waste  of  energy  and  space; 
and  yet  by  the  neglect  of  this  one  condition,  the  investigator  throws 
away  the  only  opportunity  of  adequately  analyzing  his  data. 

The  Standard  Deznation  of  an  Average. — The  element  of  un- 
certainty in  the  interpretation  of  an  average  gain  in  weight  for  a 

"Scientia,  vol.  10  (1911),  p.  106. 

"Journ.  Agr.  Sci.,  vol.  3,  pp.  417-440.     1908-10. 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  475 

lot  of  animals  is  due  to  the  fact  that  successive  lots  treated  simi- 
larly for  a  given  period  will  necessarily  give  different  average 
gains  in  weight.  An  arithmetic  mean  of  a  series  of  gains  in 
weight  must  be  considered  as  possessing  a  variability,  just  as  is 
the  case  with  the  individual  gains,  due  to  uncontrolled  experi- 
mental conditions ;  and,  since  these  uncontrolled  experimental  con- 
ditions find  direct  expression  in  the  variability  of  gains  within  the 
lot,  it  follows  that  the  variability  of  an  average  gain  bears  a  defin- 
ite relation  to  the  variability  of  individual  gains.  Obviously,  the 
variability  of  an  average  gain  decreases  as  the  size  of  the  lot  in- 
creases, the  main  reason  for  increasing  the  size  of  a  lot  being,  in 
fact,  to  render  the  average  gain  more  significant.  It  may  be 
shown,  however,  that  the  variability  of  an  average  gain  does  not 
decrease  directly  as  the  number  of  animals  in  the  lot  increases, 
but  only  as  the  square  root  of  this  nimiber  increases.^  In  other 
words,  tJie  presumptive  standard  deviation  of  an  average  gain  of 
a  lot  is  equal  to  the  standard  deviation  of  the  gains  zi'ithin  the  lot 
divided  by  the  square  root  of  their  number. 

The  Frequency  Distribution  of  an  Average. — It  may  further 
be  shown  that  the  variation  to  which  a  mean  gain  in  weight  is  sub- 
jected as  successive  samples  of  animals  are  taken  and  treated  experi- 
mentally is  such  that  the  distribution  of  means  tends  to  assume  the 
normal  form,  definable  by  the  normal  frequency  curved  such  as 
that  shown  in  Fig.  6  of  the  chart.  In  fact,  whether  the  original 
values  from  which  a  mean  is  derived  are  so  distributed  or  not,  it 
may  be  shown  that  the  distribution  of  means  tends  strongly  to  as- 
sume the  normal  fomi.  Xow,  in  conceiving  of  the  frequency  dis- 
tribution which  would  be  exhibited  by  a  particular  average  gain 
obtained  experimentally  if  tb.e  experiment  should  be  repeated  a 
large  number  of  times,  obviously  the  best  value  to  assume  for 
the  maximum  point  in  the  distribution,  the  point  of  greatest  fre- 
quency, is  the  actual  average  gain  obtained,  since  the  one  experi- 
ment actually  performed  has  indicated  that  this  is  the  most  prob- 
able value  that  would  be  obtained  upon  repetition. 

The  Probable  Error  of  an  Average. — Let  the  normal  curve  in 
•Fig.  6  of  the  chart  represent  the  presumptive  distribution  of  the 
average  gain  of  a  given  lot  of  animals.  The  mid-ordinate  of  the 
curve  we  will  assume  to  be  located  at  this  mean  value.  Now,  in 
defining  the  significance  of  such  a  mean  value,  the  following  pro- 
cedure is  the  customary  and  perhaps  the  most  natural  one  to  pur- 
sue. Divide  the  area  under  the  curve  into  two  equal  parts,  one 
part  symmetrically  including  the  maximum  ordinate  of  the  curve. 

"Yule :    "Theon-  of  Statistics."  p.  340. 

•"See  Henderson :  "Frequency  Curves  and  ^foments."  Trans.  Actuarial 
Soc.  of  Amer.,  vol.  S,  pp.  30-42. 


476  Bulletin  No.  165  [July, 

This  has  been  clone  in  the  figure,  and  that  half  of  the  area  situated 
at  the  center  of  the  distribution  is  indicated  by  cross-hatching. 
Now,  since,  as  explained  above,  areas  under  a  frequency  curve 
represent  frequencies,  it  may  be  said  that  upon  continued  repetition 
of  the  experiment,  as  many  average  lot  gains  will  fall  within  the 
shaded  area  as  without.  Expressed  in  other  terms,  the  odds  in 
favor  of  obtaining  a  second  average  gain  within  the  shaded  area, 
or  without,  for  that  matter,  are  i  to  i.  The  distance  on  the  hori- 
zontal scale  from  the  center  of  the  distribution  to  the  ordinate 
on  either  side  defining  the  shaded  area  is  known  as  the  prob- 
able error  of  the  mean,  so  that  the  probable  error  may  be  said 
to  define  an  ititerral,  syiniuetrically  including  the  average,  such 
that  the. odds  are  exactly  even  that  a  second  average  resulting  upon 
repetition  of  the  experiment  will  fall  itnfhin  it.  One  of  the  prop- 
erties of  the  normal  frequency  cun^e  is  that  the  probable  error  of 
the  mean  is  obtainable  directly  from  the  standard  deviation  of  the 
mean  by  simply  multiplying  by  the  factor  0.6745,^  from  which  it 
follows  that  the  probable  error  of  an  az'erage  lot  gain  in  weight  is 
equal  to  the  standard  deviation  of  the  average  multiplied  by  0.6745, 
or  is  equal  to  the  standard  deviation  of  the  indiz'idnal  gains  tmthin 
the  lot  divided  by  the  square  root  of  their  ntunber  and  midtiplied 
by  the  factor  0.6745}^ 

A  very  good  statement  of  the  relation  between  the  three  statis- 
tical constants  thus  far  discussed  is  given  by  H.  L.  Rietz  in  his 
Appendix  to  Eugene  Davenport's  "Principles  of  Breeding."  Rietz 
says:  "In  describing  a  frequency  distribution,  the  average  gives 
absolutely  no  idea  as  to  whether  deviations  are  large  or  small, — 
nothing  in  regard  to  the  spread  of  the  distribution.  It  is  the  ob- 
ject of  the  'standard  deviation'  to  be  descriptive  of  this  variabilit}^, 
and  it  is  the  object  of  the  so-called  'probable  error'  to  indicate 
what  confidence  is  to  be  placed  in  statistical  results."  The  descrip- 
tion of  a  series  of  gains  made  by  a  lot  of  similarly  treated  ex- 
perimental animals  should  be  thought  of  as  a  more  or  less  com- 
plete and  satisfactory  description  of  the  frequency  distribution  of 
gains  of  which  the  particular  series  experimentally  obtained  is  a 
random  sample. 

The  Limits  of  Practical  Certainty. — The  ordinates  situated  at 
distances  from  the  center  of  the  curve  of  two  and  three  times  the 
probable  error  are  also  indicated  in  Fig.  6.  The  first  pair  of  or- 
dinates include  nine-elevenths  of  the  area  of  the  curve,  or  the  ratio 
of  the  area  within  the  ordinates  to  the  area  without  is  4.5  to  i ; 

"Yule :    "Theory  of  Statistics,"  pp.  305-307. 

"•The  probable  error  of  the  mean  may  be  expressed  mathematically  by  the 

formula      Em =0.6745      ;=■  where  a  is  the  standard  deviation  of  the  original 
observations  and  n  is  their  number. 


lyis]  Unckktaixtv  in  Interpretatiun  of  Feeding  Experiments  477 

from  whicli  it  follows  that  the  odds  of  obtaining  a  second  average 
gain  within  a  distance  of  twice  the  probable  error  from  the  aver- 
age actually  obtained  are  4.5  to  i.  Similarly,  for  a  distance  of 
three  times  the  probable  error,  the  odds  are  about  21  to  i,  for  four 
times  the  probable  error,  142  to  i,  for  five  times  the  probable  er- 
ror, 13 10  to  I,  etc.^  Since  there  are  no  definite  limits  to  a  dis- 
tribution of  this  kind,  the  occurrence  of  average  gains  upon  repe- 
tition of  the  experiment  extremely  removed  from  the  average  gain 
actually  obtained,  which  is  represented  by  the  mid-ordinate  of 
the  curs'e,  cannot  be  said  to  be  impossible,  but  only  extremely 
improbable.  It  becomes  necessary,  therefore,  in  assigning  the  sig- 
nificance of  an  average  lot  gain,  to  decide  upon  some  value  which, 
when  added  to  and  subtracted  from  the  average  gain,  defines  an 
interval  such  that  the  average  gain  obtained  upon  repeating  the 
experiment  is  practically  certain  to  fall  within  it.  Wood  and  Strat- 
ton  have  recommended  that  for  data  obtained  from  agricultural 
experiments  that  pair  of  ordinates  situated  equidistant  from  the 
mid-ordinate  of  the  frequency  curve  and  removed  from  it  to  such 
a  distance  that  the  area  between  them  and  the  curve  constitutes 
30/31  of  the  total  area  under  the  curve,  are  good  limiting  values 
for  use.  This  merely  amounts  to  assuming  that  when  the  odds 
are  30  or  more  to  i  that  an  event  will  happen,  we  are  practically 
certain  that  it  will  happen.  For  a  normal  distribution,  which,  as 
has  been  seen,  an  average  lot  gain  tends  to  assume,  a  value  3.17 
times  the  probable  error,  or,  roughly,  3  times  the  probable  error, 
constitutes  the  limiting  value  recommended  by  \\'ood  and  Stratton. 
The  requirement  of  odds  of  at  least  30  to  i  that  a  feeding  ex- 
periment upon  repetition  will  duplicate  the  results  actuallv  ob- 
tained, before  definite  conclusions  be  drawn  from  it  and  definite 
recommendations  be  made  to  the  farmer,  seems  reasonable  and, 
judging  from  the  current  practice  of  the  investigators  in  various 
fields  employing  these  methods,  is  not  by  any  means  severe.  Thus, 
Davenport  and  Rietz,  in  Bulletin  119  of  this  station,  say:  "It  will 
be  noticed  that  by  the  time  we  have  made  an  allowance  of  three  or 
four  times  the  probable  error  we  have  reached  a  chance  which 
amounts  to  practical  certainty  and  even  21  to  i  involves  far  less 
chance  than  is  inz'oh'cd  in  most  business  transactions/' 

The  merit  of  such  methods  as  these  for  the  interpretation  of 
feeding  trials  consists  largely  of  the  fact  Ci)  that  thev  are  per- 
fectly systematic,  (2)  that  the  argument  leading  from  the  origi- 
nal individual  data  to  the  resulting  conclusions  is  unbroken  and 
capable  of  being  expressed  definitely,  and   (3)  that  after  it  is  de- 

°C.  B.  Davenport:  "Statistical  Aiethods."  p.  14.  New  York.  John  Wiley  & 
Sons,  2nd  rev.  ed.     1904. 


478  Bulletin  No.  165  [July, 

cided  that  the  methods  are  applicable,  the  personal  judginent  of  the 
investigator,  which  is  so  liable  to  introduce  bias  into  the  interpre- 
tation, is  practically  eliminated. 

Illustrations  of  the  Use  of  the  Probable  Error 

In  illustrating  the  use  of  the  probable  error  we  will  first  con- 
sider an  experiment  published  in  Bulletin  71  of  the  South  Dakota 
Station,  the  object  of  which  w^as  to  compare  the  value  of  speltz 
and  barley  as  a  single  grain  ration  for  fattening  sheep.  The 
two  lots  consisted  of  12  animals  each.  Lot  I,  fed  speltz,  made  an 
average  gain  during  the  105  days  of  the  experiment  of  25.0  lbs. 
per  sheep.  The  standard  deviation,  of  the  gains  in  this  lot  was 
9.44  lbs.  From  these  figures,  the  best  estimate  we  can  make  of 
the  standard  deviation  that  would  be  exhibited  by  the  average  gain 
if  the  experiment  were  repeated  a  large  number  of  times  is  9.44 
lbs,  divided  by  1/T2  (there  being  12  sheep  in  the  lot),  which 
is  equal  to  2.73  lbs.  Since  the  distribution  of  such  a  series  of 
average  gains  would  be  of  the  normal  type,  the  probable  error  of 
the  average  gain  obtained  in  this  experiment  is  equal  to  its  stand- 
ard deviation,  2.73  lbs.,  multiplied  by  the  factor  0.6745,  the  re- 
quired product  being  1.8  lbs.  The  average  g'ain  with  its  probable 
error  is  ordinarily  written  25.0  ±  1.8  lbs.,  and  the  whole  expres- 
sion means  that  the  odds  are  exactly  even  that  if  the  experiment 
were  repeated  with  12  other  sheep  fed  a  grain  ration  of  speltz  and 
treated  in  all  other  ways  as  far  as  possible  the  same  iis  were  the 
sheep  in  this  experiment,  the  mean  gain  for  the  lot  wovild  fall  with- 
in the  interval  25.0-1.8  lbs.^23.2  lbs.,  and  25.0+1.8  lbs.=26.8 
lbs.  Similarly  the  odds  are  30  to  i  that  this  second  average  gain 
would  fall  within  the  interval  25.01^(3.17X1.8)  lbs.,  that  is,  some- 
where between  19.3  lbs  and  30.7  lbs.  Thus,  while  the  average  gain 
actually  obtained  was  25.0  lbs.,  and  while  this  is  the  most  probable 
average  gain  that  would  be  obtained  upon  repetition  of  the  experi- 
ment, we  can  say  witli  reasonable  certainty  only  that  a  second  aver- 
age gain  would  fall  somewhere  between  19.3  and  30.7  lbs.  Thus,  the 
element  of  uncertainty  resulting  from  the  meaningless  fluctuations 
in  the  gains  of  the  individual  sheep  due  to  the  individuality  of  the 
animals  and  other  uncontrolled  experimental  conditions,  has  been 
fairly  definitely  and  reasonably  defined  for  this  lot  of  animals. 

Lot  II,  fed  a  grain  ration  of  barley,  yielded  an  average  gain  of 
37.9  lbs.,  the  standard  deviation  of  the  individual  gains  being  8.23 
lbs.  Proceeding  as  above,  the  probable  error  of  this  average  gain 
will  be  found  to  be  1.6  lbs.,  so  that  we  are  practically  certain  that 
a  second  average  gain  which  would  result  from  repeating  the  ex- 
periment on  other  sheep,   would   fall   within   the   interval  37.9^1 


iQjj]  Uncertainty  in  Interpretation  of  Feeding  Experiments  479 

(3.17X1.6)  lbs.,  namely,  between  the  limits  32.8  lbs.  and  43.0  lbs. 

Therefore,  since  we  are  practically  certain  that  any  random 
sample  of  12  sheep  selected  as  were  the  sheep  of  this  ex[x;riment 
and  treated  as  was  Lot  I,  wonld  exhibit  an  average  gain  in  105 
days  between  19.3  and  30.7  lbs.,  and  that  any  similarly  selected 
sample  of  12  sheep  treated  as  was  Lot  II  wonld  show  an  average 
gain  in  105  days  between  32.8  lbs.  and  43.0  lbs.,  it  is  obvious  that 
we  may  feel  sure  that  the  one  deliberate  difference  in  treatment 
between  Lots  I  and  II,  i.  e.,  the  difference  in  grain  ration,  does 
influence  the  gain  in  weight  of  sheep,  barley  tending  to  produce  a 
better  gain  than  speltz  under  the  feeding  conditions  of  this  experi- 
ment. A  more  systematic  way  of  settling  the  question,  however, 
is  to  take  the  difference  in  average  gain  between  the  two  lots,  i.e., 
12.9  lbs.,  and  find  its  probable  error.  It  may  be  shown  that 
the  presumptive  variability  or  standard  deviation  that  would  be 
exhibited  by  a  difference  between,  two  averages  if  the  experiment 
were  repeated  over  and  over  again,  is  equal  to  the  square  root  of  the 
sum  of  the  squares  of  the  standard  de\iations  of  both  averages,^ 
and  consequently  the  probalile  error  of  a  difference  bears  a  like  re- 
lation to  the  probable  errors  of  the  two  averages.  According  to 
this  formula,  the  probable  error  of  the  difference  under  considera- 
tion is  2.4  lbs.,  so  that  we  may  feel  certain  that  upon  repetition, 
the  excess  of  gain  of  the  barley  lot  over  that  of  the  speltz  lot 
would  be  within  the  limits  12.91^(3.17X2.4)  lbs.,  that  is,  between 
5.3  and  20.5  lbs.  The  average  difference,  12.9  lbs.,  is  5.4  times  its 
probable  error,  and  the  odds  that  the  excess  average  gain  of  Lot 
II  over  that  of  Lot  I  would  fall  between  o  and  25.8  lbs.  are  over 
70CXD  to  I. 

In  Bulletin  64  of  tlie  Pennsylvania  Station  is  reported  an  ex- 
periment on  steers,  one  of  the  purposes  of  which  was  to  compare 
the  gains  made  by  steers  fed  during  the  winter  in  a  barn  with  those 
made  by  steers  fed  in  an  open  shed  adjoining  an  open  yard.  The 
lots  contained  12  steers  each  and  were  treated  alike  except  as  re- 
gards shelter.  Lot  I,  fed  in  a  barn,  showed  an  average  gain  in 
126  days  of  267.71^8.8  lbs.,  and  Lot  II,  fed  in  an  open  shed,  a 
gain  of  247.71^7.4  lbs.  The  difference  in  gain  between  the  two 
lots  was  19.0=^11.5  lbs.  Since  this  difference  is  less  than  twice  its 
probable  error,  it  may  well  have  resulted  from  the  casual  factors 
producing  variation  within  the  lot. 

In  the  i6th  Annual  Report  of  the  Wisconsin  Station,  the  re- 
sults of  an  experiment  to  determine  the  comparative  value  of  rape 
and  clover  for  growing  young  pigs  is  reported.  Each  lot  of  pigs 
contained  21  animals.     During  an  experimental  period  of  56  days, 

*Yule:     "Theory  of  Statistics,"  pp.  207-208. 


480  Bulletin  No.  105  [Jtdy, 

Lot  I,  which  was  pastured  on  rape,  gained  yi.o±.i.4  lbs.,  and  Lot 
II,  pastured  on  clover,  68.3±:i.3  lbs.,  the  difference  in  favor  of 
Lot  I  being  2.7=1=1.9  lbs.  The  odds  are  only  2  to  i  that  upon  re- 
petition of  the  experiment  the  lot  pastured  on  rape  would  exhibit 
a  gain  between  o  and  5.4  lbs.  above  that  of  the  lot  pastured  on 
clover,  and  it  may  be  shown  by  taking  the  ratio  of  the  difference 
in  gain  to  its  standard  deviation  and  using*  tables  of  the  normal 
probability  integral,^  that  the  odds  are  only  5  to  i  that  under  the 
conditions  of  this  experiment  rape-pastured  pigs  would  again  ex- 
hibit a  greater  average  gain  than  clover-pastured  pigs.  Thus, 
the  data  when  analyzed  by  the  method  under  discussion  hardly 
warrant  a  definite  conclusion, 

A  Probability  Method  for  Small  Lots  of  Animals 

\Miile  the  calculation  of  probable  errors  and  the  use  of  tables 
of  normal  probability  integrals  is  the  best  method  available,  and 
is  undoubtedly  a  good  method  for  precise  definition  of  the  element 
of  uncertainty  inherent  in  the  interpretation  of  averages  when  the 
number  of  animals  per  lot  is  large,  when  the  number  is  ten  or 
less,  a  probability  table  compiled  by  "Student"  and  published  in 
Biometrika^  for  1908  may  better  be  used  for  this  purpose.  In  the 
article  in  which  the  table  occurs,  "Student"  considers  the  distribu- 
tion of  means  of  small  samples  and  finds  certain  irregularities 
Avhich  gradually  disappear  as  the  size  of  the  sample  increases. 
These  discrepancies  between  the  theory  of  large  samples  and  the 
theory  of  small  samples  are  such  that  by  the  application  of  the  or- 
dinary theor}-  which  has  been  described  above,  to  small  samples, 
i.  e.,  samples  of  ten  or  less,  the  odds  obtained  that  repetition  will 
result  in  a  certain  way  are  greater  than  the  data  actually  justify. 
The  methods  of  analysis  described  in  this  article  should  commend 
themselves  highly  to  the  investigator  who  is  compelled  for  practical 
reasons  to  employ  small  lots  of  animals. 


»C.  B.  Davenport :     "Statistical  Methods,"  p.  119. 
"Page  1. 


JQIS]  Uncertainty  in  Interpretation  of  Feeding  Experiments  481 

PART  II.     A  STATISTICAL  STUDY  OF    VARIATION  IN 

THE  GAINS  IN  WEIGHT  OE  FARM  ANIMALS 

UNDER  LIKE  CONDITIONS 

Introduction 

In  the  preceding  section  of  this  bulletin,  it  is  shown  that  an 
important  factor  contributing  to  the  element  of  uncertainty  in  the 
interpretation  of  feeding  trials  consists  of  individual  differences 
in  the  reaction  of  experimental  animals  to  environmental  conditions 
and  of  the  unavoidable  differences  in  environmental  conditions  to 
which  the  different  experimental  animals  are  subjected.  It  is 
further  shown  that  such  a  factor  of  uncertainty  can  be  handled 
satisfactorily  by  the  ordinary  statistical  methods, — standard  devia- 
tions and  probable  errors,  as  well  as  average  gains  in  weight,  being 
calculated  for  the  different  lots  of  animals  in  a  feeding  experiment. 

With  the  advent  of  an  adequate  quantitative  measure  of  varia- 
tion in  the  gains  in  weight  of  animals  upon  like  rations  and  under 
similar  experimental  conditions,  the  possibility  presents  itself  of 
solving  many  problems  intimately  concerned  with  the  methods  of 
conducting  feeding  experiments  and  with  the  improvement  of  such 
methods.  Other  problems  possessing  a  more  general  significance 
are  also  brought  within  reach  of  definite  solution  by  the  use  of 
statistical  measures  of  variation. 

This  section  of  the  bulletin  treats  of  the  extent  of  variation  in 
gain  in  weight  within  the  lot  and  upon  what  this  variation  depends. 
Also,  the  cjuestion  of  the  reduction  of  such  variation  receives 
attention.  Finally,  consideration  is  given  to  the  possibility  that 
other  than  casual  sources  of  variation  in  gain  in  weight  are  con- 
cerned in  the  ambiguity  attaching  to  experimental  conclusions  as 
ordinarily  formulated. 

The  material  for  the  following  investigation  was  gathered 
largely  from  experiment  station  work  in  this  country,  tho  some 
valuable  assistance  was  received  from  similar  work  in  Canada  and 
England.  In  thus  utilizing  experimental  results  collected  by  many 
different  investigators  at  widely  varying  localities  for  the  purpose 
of  solving  diverse  problems  in  live-stock  feeding,  many  difficulties  , 
were  encountered  in  adapting  such  a  heterogeneous  mass  of  data 
to  the  solution  of  a  few  related  problems,  the  existence  of  which 
was  in  no  case  recognized  when  the  experiments  were  planned  and 
undertaken.  The  facts  or  suggestions  finally  elicited,  however, 
are  perhaps  the  more  valuable  because  of  the  richness  and  hetero- 
geneity of  the  results  upon  which  they  are  based. 

/.  B.  Lazves  on  Variation. — The  existence  of  extreme  varia- 
tion among  the  gains  in  weight  obtained  within  similarly  treated 


482  ButLETiN   Xo.  165  [July, 

lots  of  animals  has  ver}^  frequently  been  the  occasion  for  comment 
in  experiment  station  literature.  One  of  the  best  discussions  on 
this  subject  that  we  have  been  able  to  find  is  that  of  J.  B.  Lawes, 
occurring  in  the  course  of  a  report  of  investigations  on  the  com- 
parative fattening  qualities  of  sheep  conducted  at  the  Rothamsted 
Station,  England,  about  sixty  years  ago.  Speaking  of  the  selection 
of  the  40  Hampshire  and  40  Sussex  wethers  under  investigation, 
Lawes  says : 

"It  is  perhaps  seldom  that  animals  have  been  drawn  for  purposes  of  ex- 
periment with  more  care  than  in  the  instances  of  which  the  foregoing  tables 
[giving  the  weights  and  gains  of  the  sheep]  record  the  results,  yet  we  have 
scarcely  a  sheep  in  either  breed  which  does  not  give  twice,  thrice,  or  more 
times  as  great  an  increase  in  gross  live  weight  at  one  period,  as  at  another  of 
equal  length;  whilst  taking  the  entire  period  of  the  experiment,  we  have  nearly 
double  the  increase  with  some  animals  as  with  others  by  their  side,  and  having 
ostensibly  the  same  description  and  qualities  of  food  provided. 

"The  variation  in  the  apparent  rate  of  gain  of  the  same  animal  at  different 
times,  is  largely; due  to  the  difference  in  the  amounts  of  the  matters  of  the  food 
retained  within  the  animal  at  the  different  times  of  weighing,  and  to  obviate 
error  from  this  cause  we  have  only  to  extend  our  experiments  over  a  sufficient 
length  of  time,  and  to  be  careful,  as  far^  as  possible,  always  to  weigh  the  ani- 
mals at  the  same  period  of  the  day,  and  under  similar  circumstances  as  regards 
their  hours  of  feeding. 

"With  respect  to  the  difference  of  result  shown  by  different  animals,  hav- 
ing professedly  the  same  allowance  of  food,  much  of  it  is  doubtless  due  to 
distinct  constitutional  tendency  to  fatten  or  otherwise;  yet  in  some  cases  it  no 
doubt  depends  upon  a  real  difference  in  the  food  consumed  by  individual  ani- 
mals, for  it  is  impossible  to  secure  for  each  its  due  share  of  the  several  foods 
supplied;  and  wherever  there  are  many  animals  kept  and  fed  together,  there  are 
always  some  who  exercise  a  kind  of  mastery  over  the  rest,  and  if  they  do  not 
eat  more  food  altogether  than  is  allotted  to  them,  they  will  at  least  take  more 
of  the  best  of  it  than  is  their  share,  and  thus  reduce  the  fair  allowance  to  all 
the  rest.  By  this  cause,  indeed,  it  is  not  improbalde  that  the  proper  feeding  and 
increase  of  some  animals  well  adapted  for  it  may  be  prevented ;  though  in  so 
far  as  these  differences  are  really  due  to  the  quantities  of  feed  consumed  by 
different  individuals,  it  is  obvious  that  the  true  relation  of  food  to  increase 
will  be  less  misstated  by  the  gross  numerical  results  of  feeding  experiments, 
than  would  be  the  case  were  the  irregularites  entirely  owing  to  varying  consti- 
tutional capabilities  of  the  different  animals  to  grow  or  fatten  upon  the  same 
food. 

"But  whatever  be  the  causes  of  these  variations,  the  figures  in  the  tables 
show  that,  notwithstanding  the  careful  selection  of  the  animals,  we  have  among 
the  Hampshire  sheep  a  difference  in  their  average  weekly  gain  of  from  about 
3M  lbs.  to  little  more  than  2  lbs.;  and  among  the  forty  Sussex  sheep,  of  from 
little  more  than  2i<  lbs.  to  less  than  1'^  lbs.  Indeed,  the  tenor  of  all  published 
results  on  feeding  seems  to  show  that  these  fluctuations  and  variations  are  the 
rule  and  not  the  exception ;  and  the  fact  of  them,  therefore,  should  lead  us  to 
'great  caution  in  drawing  nice  conclusions  from  experiments  made  with  but  a 
small  number  of  animals,  and  extending  only  over  a  short  period  of  time."* 

The  Coefficient  of  Variation. — As  is  shown  in  the  first  section  of 
this  bulletin,  the  standard  deviation,  or  root-mean-s(|uare  deviation 
from  the  arithmetic  mean,  is  a  good  measure  of  variation  for  some 
purpose,  e.g.,  for  gauging  the  value  of  the  arithmetic  mean  as  an 
approximation  to  the  typical  gain  in  live  weight  under  certain  defi- 

'Journ.  Roy.'Agr.  Soc.  of  England,  vol.  12,  pp.  419-420.     1851. 


w 


■fp^J] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


483 


nite  experimental  conditions,  or,  as  some  prefer  to  consider  it,  for 
gauging  the  value  of  the  mean  as  a  quantity  descriptive  of  a  given 
series  of  gains  in  weight  obtained  under  similar  conditions,  or, 
again,  for  measuring  the  significance  of  a  mean  gain  in  weight. 

For  extensive  comparison,  however,  the  standard  deviation  is 
inadequate,  since,  in  the  first  place,  it  depends  upon  the  units  of 
weight  employed,  and,  in  the  second  place,  it  depends  in  some 
measure  upon  the  mean  value  itself.  Thus,  a  lot  of  19  pigs  gained 
an  average  of  35.74  lbs.  in  four  weeks,  and  of  77.11  IIds.  in  eight 
weeks.  The  standard  deviation  of  the  19  individual  gains  at  the 
end  of  four  weeks  was  5.31  lbs.,  and  at  the  end  of  eight  weeks, 
11.28  lbs.  In  view  of  the  great  disparity  between  the  correspond- 
ing average  gains,  the  question  whether  the  19  pigs  exhibited  gains 
more  variable  at  the  end  of  four  weeks  than  at  the  end  of  eight 
weeks,  cannot  be  settled  in  fairness  by  comparing  simply  the  two 
standard  deviations.  For  the  fairest  comparison  it  is  customary  to 
convert  the  standard  deviations  into  percentages  based  upon  their 
respective  averages.  For  example,  5.31  constitutes  14.86  percent 
of  35.74,  and  11.28  constitutes  14.63  percent  of  77.11 ;  from  which 
it  follows  that  the  variability  for  the  two  periods  figured  in  this 
manner  was  practically  identical.  The  percentages  thus  obtained, 
i.e.,  14.86  and  14.63,  are  known  as  coefficients  of  variation,  or 
coefficients  of  variability. 

Again,  consider  a  comparison  as  to  variability  of  gain  among 
lots  of  different  species  of  animals.  Consider,  for  instance,  (i)  a 
lot  of  9  cockerels,  (2)  a  lot  of  16  sheep,  (3)  a  lot  of  21  pigs,  and 
(4)  a  lot  of  15  steers,  concerning  which  the  following  statistical 
data  have  been  collected : 


Lot 

Average 
daily  gain 

Standard 
deviation 

Coefficient 
of  variation 

1 
2 

3 

4 

.589    oz. 

.3.50   lb. 
1 .  22     lb. 
2.53      lb. 

.119     oz. 
.0451   lb. 
.157     lb. 
.242      lb. 

20.20 

12.  P9 

12.86 

9.56 

In  such  cases  as  the  above,  the  only  feasible  method  of  com- 
parison is  to  consider  the  coefficients  of  variation. 


Coefficients  of  Variation  Ordinarily  Obtained  in  Feeding 

Experiments 

Results  of  Wood  and  Stratton. — It  is  a  matter  of  some  interest 
to  study  the  variation  in  gain  in  weight,  or  the  experimental  error, 
ordinarily  existing  within  the  lot  for  the  different  kinds  of  farm 
animals.     The  only  published  investigations  of  this  nature  that  we 


484  Bulletin  No.  1G5  [Jidy, 

are  aware  of  are  those  of  Wood  and  Stratton  and  of  Robinson  and 
Hainan  referred  to  at  the  beginning  of  this  bulletin.  As  the  result 
of  nine  experiments  on  the  fattening  of  cattle  performed  at  Cam- 
bridge and  involving  90  animals,  Wood  and  Stratton  found  an 
average  coefficient  of  variation  of  21.20.  Five  similar  experiments 
performed  in  Scotland  and  involving  50  animals  gave  an  average 
coefficient  of  20.75,  while  two  cattle-feeding  experiments  performed 
in  this  country,  involving  40  animals,  yielded  an  average  coefficient 
of  variation  of  20.31.  Finally,  seven  experiments  performed  at 
Norfolk  on  the  fattening  of  sheep,  involving  100  animals,  gave  an 
average  coefficient  of  21.21.  These  four  coefficients,  three  ob- 
tained with  cattle  and  one  with  sheep,  exhibit  a  remarkable  agree- 
ment and  would  seem  to  indicate  that  for  these  two  kinds  of 
animals  the  percentage  variability  as  regards  gain  in  weight  for 
animals  within  the  lot  is  substantially  the  same. 

Results  of  Rohmson  and  Hainan. — As  the  result  of  a  statistical 
analysis  of  three  feeding  experiments,  Robinson  and  Hainan  con- 
clude that  "the  probable  error  of  one  animal  in  a  pig-feeding  ex- 
periment is  in  the  region  of  10  percent  of  the  average  live-weight 
increase."^  This  is  equivalent  to  asserting  that  the  coefficient  of 
variation  of  gains  in  weight  in  pig-feeding  experiments  is  about 
15,  a  value  considerably  lower  than  the  coefficients  of  Wood  and 
Stratton  for  sheep  and  cattle. 

Results  Obtained  from  American  B.rperiments. — Results  which 
we  have  obtained  from  experiment  station  work  performed  in  this 
country  entirely  are  slightly  different  from  those  just  quoted.  From 
the  results  of  sixteen  experiments  on  the  feeding  of  sheep,^  in- 
volving 803  animals  divided  into  80  lots  of  5  to  16  animals  each, 
we  found  the  average  coefficient  of  variation  of  the  80  coefficients 
calculated,  to  be  21.63,  a-  figi^ire  comparing  favorably  with  the  aver- 
age coefficient  of  21.20  obtained  by  Wood  and  Stratton  for  sheep. 

Eighteen  experiments  on  steers,*^  involving  449  animals  divided 
into  50  lots  of  5  to  15  animals  each,  yielded  an  average  coefficient  of 
variation  of  16.73.  This  is  considerably  lower  than  the  three  aver- 
ages for  steers  obtained  by  Wood  and  Stratton,  i.e.,  21.20,  20.75, 
and  20.31. 

From  seventeen  experiments  on  swine,"^  involving  507  pigs  di- 
vided into  49  lots  of  5  to  23  pigs  each,  an  average  coefficient  of 
17.12  was  obtained.  This  coefficient  agrees  well  with  that  obtained 
for  steers,  i.  e.,  16.73,  but  is  somewhat  higher  than  that  found  by 
Robinson  and  Hainan  for  swine. 


"Loc.  cit. 

"See  Appendix,  pages  558  to  560. 
'See  Appendix,  pages  563  to  564. 
"See  Appendix,  pages  567  to  569. 


■^p-fi] 


UlS'CERTAINTY    IN    IxTERPRETATIOK    OF    FEEDING    EXPERIMENTS 


485 


The  coefficients  here  reported  would  appear  to  indicate  that  the 
variabihty  of  gains  in  weights  for  steers  and  for  swine  are  substan- 
tially the  same,  whereas  the  variability  for  sheep  is  distinctly  higher*. 

Results  Obtained  at  IVobiini  and  Rothamstcd. — Experiments 
performed  at  the  Woburn  Experimental  Farm  and  at  the  Rotham- 
sted  Station^  tend  to  substantiate  the  conclusion  that  as  a  general 
rule  sheep  give  more  variable  gains  than  steers.  Eight  experiments 
performed  on  sheep  at  the  Woburn  Experimental  Farm,  involving 
375  animals  divided  into  25  lots  of  10  to  24  animals  each,  gave  an 
average  coefficient  of  variation  of  20.80.  If  live  experiments  per- 
formed at  the  Rothamsted  Station,  involving  316  sheep  divided  into 
15  lots  of  5  to  46  animals  each,^  be  included,  an  average  coefficient 
of  20.40  results.  Nine  experiments  on  steers  performed  at  \\  oburn, 
involving  22  lots  of  4  steers  each  and  2  lots  of  6  steers  each,  i.  e., 
a  total  of  100  steers,  gave  an  average  coefficient  of  variation  of 
18.15,  o^'^r  2  percent  lower  than  the  two  coefficients  for  sheep 
given  above. 

Discrepancies  Among  Coefficients. — Upon  reference  to  the  Ap- 
pendix, which  gives  in  tabular  form  all  of  the  data  upon  which 
the  above  discussion  is  based,  it  will  be  seen  that  the  percentage 
variability  of  the  individual  lots  varies  in  a  remarkable  manner. 
This  is  shown  by  the  following  frequency  distributions  of  the  co- 
efficients of  variation  of  the  various  lots  of  animals,  including  both 
English  and  American  experiments. 


Kind  of 

Class  intervals 

animal 

0-5 

1 
0 
0 

5-10 

10-15 

23 
16 
17 

15-20 
36 
13 
24 

20-25 
27 
8 
13 

25-30 

12 
0 

3 

30-35 
9 
0 

1 

35-40 

3 
1 
2 

40-45 
0 
0 
0 

45-50 

Sheep   

Swine   

5 

7 
12 

1 
1 

Steers    

0 

Extreme  coefficients  not  included  in  the  above  table  are :  for 
sheep,  58.21  for  a  lot  of  11  animals,  55.33  for  a  lot  of  10  animals, 
and  76.9  for  a  lot  of  5  animals;  for  steers,  51.90  for  a  lot  of  4 
animals.  The  three  distributions  tend  to  confirm  the  conclusion 
that  sheep  in  general  exhibit  greater  variability  as  regards  fatten- 
ing qualities  than  do  either  steers  or  swine. 

It  is  worthy  of  remark  that  this  extreme  variability  exhibited 
by  coefficients  calculated  from  data  obtained  from  many  separate 
lots  of  animals  treated  differently  at  different  localities  and  at  dif- 
ferent times,  is  to  be  expected,  not  only  from  the  heterogeneity  of 


'See  Appendix,  pages  561-562  and  565-566. 


486  Bulletin  No.  165  [July, 

the  data,  but  also  in  large  part  from  the  mere  size  of  the  coefficients 
obtained.  Thus,  according  to  Pearson,  the  standard  deviation  of 
a  coefficient  of  variation  C,  may  be  represented  by  the  formula 


0 


l/^/i 


^100/ 


y2 


from  which  it  follows  that  o;  increases  as  C  increases,  ti  being 
the  number  of  observations  from  which  C  is  calculated.  Thus, 
suppose  that  a  lot  of  15  sheep  exhibits  a  series  of  gains  in  live 
weight  whose  variability  is  measured  by  a  coefficient  of  20.  Then 
if  successive  series  of  sheep  taken  15  to  a  lot  were  treated  in  the 
same  manner,  the  best  estimate  we  could  make  of  the  standard 
deviation  of  the  coefficients  of  variation  obtained,  using  only  the 
data  of  the  first  series,  would  be 


20 


1  +  2  (^) 


=  3.79. 


Taking  the  probable  error  of  C  as  0.6745  o;  and  multiplying  by 
3.17,''  we  define  an  interval  symmetrically  including  the  coefficient 
20  such  that  the  odds  are  30  to  i  that  a  second  coefficient  obtained 
from  a  second  lot  of  15  sheep  would  fall  within  it.  Thus,  we  are 
practically  certain  only  that  a  second  lot  of  sheep  would  exhibit  a 
coefficient  falling  within  the  limits  20±8.i,  i.e.,  between  11.9  and 
28.1. 

Meaning  of  Such  Discrepancies. — It  is  because  of  the  large 
probable  errors  attaching  to  coefficients  of  15  to  20  that  it  is  so 
difficult  to  demonstrate  that  a  given  ration  or  other  system  of 
treatment  is  capable  of  producing  more  (or  less)  uniform  gains 
than  a  second  ration  or  other  treatment.  It  is  no  exaggeration  to 
say  that  a  single  experiment  with  lots  of  the  moderate  size  ordinari- 
ly employed  can  shed  practically  no  light  upon  a  question  of  this 
kind,  no  matter  how  extreme  the  difference  in  variation  between 
lots,  except  in  conjunction  with  other  experiments  of  a  like  nature. 

The  point  under  discussion  is  worthy  of  illustration.  Consider 
the  results  of  two  experiments  conducted  by  W.  L.  Carlyle  at  the 
Wisconsin  Station  to  determine  the  relative  value  of  rape  and 
clover  pasture  for  fattening  pigs.^  The  lots  of  pigs  employed  con- 
tained 19  animals  each  in  the  first  experiment  and  21  animals  each 
in  the  second.  In  the  first  experiment,  the  coefficient  of  variation 
of  the  gains  in  weight  of  Lot  I,  allowed  to  run  on  rape  pasture, 
was  15.50,  while  that  of  Lot  II,  turned  out  on  clover  pasture,  was 

"See  page  477. 

"iSth  and  lOth  Annual  Reports  Wis.  Sta. 


J9I3] 


UnCF.RT.\1XTY    IX    IXTERPRETATIOX    OF    FeEDIXG    ExPERIMEXTS 


487 


28.03.  One  might  conclude  from  this  experiment  that  rape  pasture 
tended  to  produce  more  uniform  gains  than  clover  pasture.  In  the 
second  experiment,  however,  the  lot  on  rape  pasture  gave  a  coeffi- 
cient of  variation  of  13.23,  while  the  lot  on  clover  pasture  gave  a 
coefficient  of  only  12.88. 

Number  of  Animals  per  Lot  Required  ix  Feeding  Experi- 
ments 

Statistical  theory  is  capable  of  attacking  directly  a  problem  of 
considerable  importance  to  the  technic  of  feeding  experiments, 
i.  c,  the  number  of  animals  that  should  be  included  in  the  lots  of 
a  feeding  experiment.  The  calculations  upon  which  Table  i,  giv- 
ing the  results  of  a  statistical  study  of  this  problem,  is  based  are 
given  in  the  Appendix.^  The  number  of  animals  required  to  dem- 
onstrate satisfactorily  the  significance  of  various  percentage  dif- 
ferences in  average  gain  in  weight  between  two  lots  of  animals, 
for  sheep  and  for  pigs  and  steers,  is  given  in  this  table,  the  sup- 
position being,  as  the  evidence  seems  to  indicate,  that  in  general, 
in  experiments  on  sheep  more  animals  are  required  per  lot  than 
in  experiments  on  swine  and  steers.  The  few  data  that  we  have 
collected  concerning  the  variability  of  the  gains  in  weight  of  poul- 
try are  quite  comparable  with  those  for  swine  and  steers,  indicating 
that  the  same  number  of  animals  per  lot  are  required  for  the  former 
as  for  the  latter. 

It  will  be  seen  from  Table  i  that  only  a  moderate  number  of 
animals  are  required  per  lot  except  for  differences  of  less  than  12.5 


Table  1. — Number  of  Aximals  per  Lot  Required  to  Demonstrate  the  Signif- 
ICAXCE  of  Various  Percextage  Differexces  Between  Average  Lot  Gains 


For  experiments  on  sheep 

For  experiments  on  steers 
and   swine 

Percentage 

difference 

between 

average 

lot  gains 

Number  of 
animals 
per  lot 
required 

Percentage 

difference 

betv.een 

average 

lot  gains 

Number  of 
animals 
per  lot 
required 

50 

40 

30 

20 

17.5 

15 

12.5 

10  • 

7.5 

5 

2.5 

2 

2 

4 

8 

10 

14 

20 

31 

54 

121 

482 

50 
•      40 
30 
20 
17.5 
15 

12.5 
10 

7.5 

5 

1 

2 

3 

5 

7 

9 

13 

20 

36 

80 

317 

'See  pages  571  to  572. 


488  Bulletin  Xo.  iGj  [Ji'ly, 

to  15  percent  between  lots.  For  differences  of  less  than  12.5  to  15 
percent  the  number  of  animals  required  increases  at  a  very  rapid 
rate. 

Advantages  of  Large  Lots  of  Animals. — In  order  to  appreciate 
the  significance  of  Table  1,  it  is  necessary  to  form  some  idea  of  the 
percentage  differences  ordinarily  obtained  between  lots  of  animals 
treated  differently.  In  the  case  of  rations  markedly  different  in 
nutritive  value,  such  as  corn  meal  alone  and  corn  meal  sui)plemented 
by  meat  meal,  shorts,  middlings,  tankage,  etc.,  in  swine  experi- 
ments, differences  between  average  lot  gains  may  run  as  high  as 
95  to  100  percent.  Experiments  comparing  the  relative  efficiency 
of  alfalfa,  timothy,  and  clover  hay,  or  of  some  of  the  more  com- 
mon grains,  or  feeding  on  pasture  and  in  dry  lot,  in  the  pro- 
duction of  gains  in  weight,  may  yield  differences  of  15  to  50 
percent  between  lots.  However,  such  cases  as  those  just  cited  are 
exceptional.  In  the  common  run  of  feeding  trials,  the  purpose  is 
to  determine  the  relative  efficiency  of  two  rations  of  approximately 
e(iual  value,  so  that  differences  of  more  than  10  to  15  percent  be- 
tween lots  are  not  to  be  expected.  Consequently,  according  to  the 
best  information  available,  the  lots  of  animals  used  should  contain 
at  least  10  to  14  animals,  if  definite  information  is  to  be  derived 
from  the  experiment.  In  fact,  for  differences  as  low  as  10  percent 
between  lots,  25  to  30  animals  are  required.^ 

Such  a  large  number  of  animals  is  rarely  used  and  is  perhaps 
prohibitive  for  most  experiments.  However,  when  working  with 
animals  whose  feeding  capacities  and  other  individual  characteristics 
are  so  variable,  and  when,  in  general,  experimental  conditions  are 
under  such  loose  control  that  the  standard  deviation  of  gains  w  ithin 
the  lot  averages  17  to  21  percent  of  the  average  lot  gain,  the  point  to 
insist  upon  is  that  the  results  of  single  experiments  with  four  or  five 
animals  are  in  general  ])ractically  worthless  except  in  conjunction 
with  other  experiments  performed  under  the  same  conditions.  This 
is  the  conclusion  to  which  Wood  and  Stratton  have  come,  and  it 
seems  to  be  inevitable,  at  least  until  some  method  of  lowering  this 
extreme  variability  is  discovered. 

In  the  course  of  the  elaborate  exj^eriments  perfonned  at  the 
Rothamsted  Station  on  the  comparative  fattening  qualities  of  dif- 
ferent breeds  of  sheep,  J.  B.  Lawes  again  and  again  calls  attention 
to  the  variability  in  fattening  qualities  exhibited  by  sheep  under 

'These  estimates  of  the  number  of  animals  pier  lot  required  in  order  to  ob- 
tain definite  information  concerning  a  problem  in  animal  feedinp;.  r^te  to  the 
feeding  experiment  as  ordinarily  run,  in  which  no  particular  effort  is  made  to 
reduce  the  experimental  error.  When  such  effort  is  made  in  an  effective  man- 
ner, perhaps  according  to  the  suggestions  hereinafter  outlined,  the  above  esti- 
mates may  be  reduced  to  a  greater  or  less  extent. 


^9^3]  L'nlektaintv  in   Interpretation  ok  Feeding  Kxpekimems  489 

supposedly  like  conditions  and  selected  with  the  utmost  care.  Thus, 
in  his  investigation  of  the  Cotswold  breed,  he  says,  in  speaking 
of  the  table  giving  the  gains  in  weight  per  four  weeks  and  for  the 
entire  experiment  of  each  of  the  46  wethers: 

"This  table  brings  prominently  to  our  view  the  point  to  which  we  have  so 
often  called  attention,  namely,  the  great  variation  in  the  rate  of  gain  of  the 
same  animal  during  different  consecutive  periods  and  of  different  animals  of 
the  same  breed,  however  carefully  selected,  and  having  ostensibh-  the  same 
description  and  qualities  of  food.  This  point  we  feel  it  is  important  to  insist 
upon  so  often,  as  showing  the  uselessness  of  comparative  experiments  on  feed- 
ing, unless  both  conducted  with  a  large  number  of  animals,  and  extended  over 
a  considerable  period  of  time,  so  as  to  eliminate,  as  far  as  possible,  the  effects  of 
the  various  sources  of  irregularity  which  we  have  before  pointed  out."* 

The  same  warning  is  given  in  the  investigation  of  Leicester 
and  crossbred  lambs.  We  wish  to  emphasize  this  attitude  of  Lawes 
as  being  assumed  over  half  a  century  ago  by  a  man  of  undoubted 
authority  in  such  matters,  as  the  result  of  an  extensive  experience 
in  the  fattening  of  sheep  and  of  other  farm  animals.  It  is  evi- 
dently an  attitude  necessarily  assumed  by  the  careful  observer  in 
practical  animal  husbandry,  as  well  as  by  the  statistical  investigator 
after  analyzing  by  methods  at  present  peculiarly  his  own  the  wealth 
of  data  which  experiment  stations  everywhere  have  rendered  ac- 
cessible to  him. 

The  necessity  of  employing  large  lots  of  animals  in  demon- 
strating the  relative  efficiency  of  two  treatments  of  approximately 
equal  value,  for  instance  two  treatments  capable  of  producing  a 
lo-percent  difTerence  in  gain  in  live  weight  between  two  lots  of 
animals,  is  capable  of  illustration  in  another  and  perhaps  more  ef- 
fective way.  Assuming  an  equal  percentage  variability  of  gains  in 
the  two  lots,  each  of  which  contains  10  animals,  this  percentage 
variability  must  be  no  higher  than  12.06  in  order  to  set  up  odds 
of  at  least  30  to  i,  that  is,  in  order  to  adequately  prove  any  differ- 
ence whatever  in  efficiency  between  two  experimental  treatments 
capable  of  effecting  a  lo-percent  difference  in  gain.  Considering 
the  American  experiments  only,  of  the  80  lots  of  sheep  whose  co- 
efficients of  variation  were  determined,  only  11  exhibited  a  varia- 
bility as  low  as  this;  of  the  49  lots  of  pigs  only  8  possessed  a 
coefficient  of  12.06  or  less;  of  the  50  lots  of  steers  only  9  gave 
coefficients  as  low  as  or  lower  than  12.06.  With  14  animals  to 
the  lot,  a  coefficient  of  variation  for  each  lot  at  least  as  low  as 
14.23  is  necessary-.  Fifteen  of  the  80  lots  of  sheep,  19  of  the  49 
lots  of  pigs,  and  15  of  the  50  lots  of  steers  possessed  coefficients  of 
variation  as  low  as  or  lower  than  14.23.  With  16  animals  to  the 
lot,  a  coefficient  of  variation  for  each  lot  of  at  most  15.26  is  re- 
quired. Sixteen  of  the  80  lots  of  sheep,  24  of  the  49  lots  of  pigs, 
and  19  of  the  50  lots  of  steers  possessed  coefficients  of  variation  as 
low  as  or  lower  than  this. 


•Journ.  Roy.  Agr.  Soc.  of  England,  vol.  13,  p.  182.    1852. 


490  Bulletin  No.  165  [July, 

Size  of  Gains  and  Their  Variabiuty 

From  inspection  of  the  data  given  in  the  Appendix,  one  receives 
the  impression  that  in  general,  for  the  same  feeding  experiment, 
there  is  a  tendency  for  the  variabihty  of  gains  witliin  the  lot  to 
correlate  itself  with  the  average  gain,  low  average  gains  being  in 
general  associated  with  high  variabilities.  The  detailed  data  are 
so  heterogeneous  as  to  render  any  systematic  study  of  this  ques- 
tion impossible.  However,  confining  ourselves  to  those  experi- 
ments in  which  the  lots  consist  of  at  least  lo  animals  and  the 
differences  among  average  lot  gains  are  large,  we  will  consider  only 
those  results  capable  of  affording  the  most  decisive  evidence  either 
one  way  or  the  other. 

Evidence  for  Sheep. — Considering  the  feeding  experiments  with 
sheep^  first,  Experiment  i  offers  little  evidence  either  one  way  or 
the  other,  the  gains  for  most  lots  being  quite  similar.  However, 
Lot  I,  with  the  lowest  average  gain  (32.9  lbs.)  exhibits  the  highest 
coefficient  of  variation  (25.08)  ;  while  Lot  IH,  wnVa  the  highest 
average  gain  (41.3  lbs.)  possesses  a  coefiicient  of  variation  of  only 
17.31.  The  standard  deviations  of  these  two  lots  stand  in  the 
same  relation  to  each  other.  In  Experiment  4,  Lot  I  (10  sheep) 
shows  an  average  gain  of  31.3  lbs.,  a  standard  deviation  of  4.80 
lbs.,  and  a  coefficient  of  variation  of  15.34;  Lot  H  (10  sheep) 
shows  an  average  gain  of  23.4  lbs.,  a  standard  deviation  of  7.79 
lbs.,  and  a  coefficient  of  variation  of  33.29.  Thus,  in  this  case  the 
lot  giving  the  lower  average  gain  exhibits  the  higher  absolute 
and  percentage  variability,  the  differences  being  very  marked. 

In  Experiment  5,  Lots  la,  Ila,  and  Ilia  were  under  experiment 
in  the  fall  of  1908,  while  Lots  lb,  lib,  and  Illb  were  under  experi- 
ment in  the  fall  of  1909,  the  lots  designated  by  the  same  Roman 
numeral  receiving  similar  rations.  It  will  be  seen  from  page  558 
of  the  Appendix,  that  much  better  gains  were  obtained  in  1908 
than  in  1909,  even  after  reduction  to  a  daily  basis;  also,  that  the 
variability  of  gains  is  greater  for  the  year  giving  the  poorer  gains 
(1909).  Furthermore,  on  comparing  Lot  Illa  with  Lots  la  and 
Ila,  Lot  Ilia  is  seen  to  have  the  greatest  average  gain  and  the 
smallest  coefficient  of  variation.  Similarly,  on  comparing  Lot  Illb 
with  Lots  lb  and  lib.  Lot  Illb  is  seen  to  possess  the  greatest  aver- 
age gain  and  the  least  absolute  and  percentage  variability. 

In  Experiment  6,  it  will  be  noted  that  Lots  I  and  III,  with  the 
lowest  average  gains,  exhibit  the  highest  absolute  and  percentage 
variability.  Lot  I,  Experiment  7,  shows  an  average  gain  of  25.0 
lbs.  in  105  days,  and  a  standard  deviation  of  9.44,  i.  e.,  2>7-77  P^^" 

"See  Appendix,  pages  558  to  562. 


/p/j]  UXCERTAIXTV    l.\    INTERPRETATION    OF    FEEDING    EXPERIMENTS  491 

cent  of  the  mean.  Lot  II  exhibits  an  average  daily  gain  of  37-9, 
a  standard  deviation  of  8.23,  and  a  coefTficient  of  variation  of  21.70, 
In  Experiment  8,  Lots  la  and  Ila  before  weaning  exhibit  much 
better  average  gains  than  after  weaning'.  The  results  in  th.e  latter 
case  are  recorded  under  Lots  lb  and  lib.  The  percentage  varia- 
bility before  weaning  is  correspondingly  less  than  that  after  wean- 


ing. 


We  shall  not  attempt  an  analysis  of  Experiment  9  because  the 
lots  are  so  small,  but  from  a  cursory  glance  at  the  results  for  the 
four  lots  before  and  after  weaning  it  will  be  seen  that  they  agree 
admirably  with  the  theory  that  the  better  gains  are  also  in  general 
the  more  uniform  gains. 

As  further  support  for  this  conclusion,  we  cite  Experiments  13, 
17,  18,  20,  23,  and  24  of  the  Appendix. 

Bindcucc  for  Szvinc. — The  experiments  on  swine^  do  not  af- 
ford very  strong  confirmation  of  the  theory  under  consideration, 
it  must  be  admitted.  This  is  due  in  large  part  to  the  fact  that  in 
many  of  the  swine  experiments  the  lots  made  similar  gains,  and 
that  in  many  experiments  small  lots  of  animals  were  employed, 
— conditions  unfaA-orable  to  the  solution  of  the  problem  at  hand. 
In  Experiment  62,  tho  the  lots  were  small,  the  inverse  correlation 
between  average  gain  and  variability  for  the  six  lots  is  very  evi- 
dent. In  Experiments  63  and  64,  with  8  and  9  animals  to  the  lot, 
the  evidence  is  more  or  less  contradictory.  In  Experiment  65,  the 
data  are  very  irregular,  tho  they  fall  in  with  the  theory  after  a 
fashion.  Thus,  the  average  coefficient  of  variability  for  the  three 
lots  giving  the  three  lowest  average  gains  is  37.9;  for  the  three 
lots  giving  the  next  lowest  gains,  16.8;  for  the  three  lots  giving 
the  next  lowest  gains,  15.8;  and  for  the  lot  giving  the  highest  gain, 
13.5.  In  Experiments  66  and  69  the  evidence  is  contradictory, 
while  in  Experiments  67  and  68,  it  is  favorable  to  the  theory.  In 
Experiment  yy,  the  evidence  is  contradictory. 

Ei'idcnce  for  Steers. — For  steers,^  conditions  are  about  the  same 
as  for  swine.  We  will  not  consider  the  Pennsylvania  experiments 
(35>  36,  37,  38,  39,  41,  and  42),  since  in  all  of  them  the  two  lots 
gave  very  similar  average  gains  in  weight.  The  most  comprehen- 
sive single  steer  experiment  the  data  for  which  are  given  in  the 
Appendix,  is  Xo.  43,  an  experiment  by  H.  W.  Mumford  performed 
at  the  ^Michigan  Station.  In  this  experiment  the  correlation  be- 
tween average  daily  gain  per  lot  and  the  coefficient  of  variation, 
while  far  from  perfect,  is  quite  perceptible.  The  two  largest  co- 
efficients obtained   are  those  for  Lots  IX  and  X,  exhibiting  the 

"See  Appendix,  pages  567  to  569. 
"See  Appendix,  pages  563  to  566, 


492  Bulletin  No.  165  [July, 

two  smallest  average  gains,  while  the  smallest  coefficient  is  that  of 
Lot  VII,  exhibiting  the  largest  average  gain.  Arranging  the  lots 
in  groups  of  two  in  the  order  of  increasing  average  lot  gains,  the 
average  coefficients  of  variation  per  group  run  as  follows:  24.15, 
16.40,  15.83,  17.00,  and  14.84, 

Evidence  for  Poultry. — Considering  next  the  poultry  experi- 
ments,^ aside  from  Experiment  78,  in  which  the  results  are  very 
irregular,  probably  because  the  lots  were  composed  of  different 
breeds,  and  Experiment  84,  in  which  there  was  only  one  lot,  all 
show  a  greater  absolute  and  percentage  variability  for  the  lot  ex- 
hibiting the  lower  average  gain.  The  unanimity  exhibited  by  these 
five  experiments  is  quite  remarkable. 

Siinimary  of  Bvidcnce. — The  preponderance  of  evidence  thus 
favors  the  conclusion  that  good  gains  are  in  general  uniform  gains, 
and  that  in  any  experiment  involving  two  or  more  lots  of  animals 
there  will  be  more  or  less  close  correlation  between  average  lot 
gains  and  the  corresponding  coefficients  of  variation,  such  that 
large  values  of  the  former  will  in  general  be  associated  with  small 
values  of  the  latter.  While  the  evidence  that  we  ha.ve  presented 
in  support  of  this  view  is  more  convincing  for  sheep  and  poultry 
than  for  steers  and  swine,  the  distinction  is  more  apparent  than 
real.  As  explained  above,  the  particular  sheep  and  poultry  experi- 
ments cited  are  more  favorable  to  a  solution  of  the  problem  than 
the  steer  and  swine  experiments.  The  conclusion  of  this  section 
may  be  stated  in  other  words,  i.  e.,  it  appears  that  experimental 
conditions  favorable  to  growth  and  fattening  are  favorable  to  uni- 
formity of  individual  gains. 

Re:duction  of  the  Expivrime^ntal  Error  in  Feeding 

Experiments 

The  question  whether  the  extreme  variability  of  gains  in  weight 
ordinarily  encountered  in  feeding  experiments,  constituting  the  ex- 
perimental error  of  such  investigations,  can  be  reduced  without 
diminishing  the  significance  of  experiment  station  work,  is  a  legiti- 
mate object  for  discussion  and  investigation.  As  the  result  of  a 
single  careful  experiment  on  four  steers.  Wood  and  Stratton  con- 
clude that  there  is  no  way  of  surmounting  the  difficulty  caused  by 
the  extreme  variability  of  gain  in  weight  of  farm  animals  and  that 
"the  requisite  precision  in  feeding  trials  can  only  be  obtained  by 
increase  of  numbers,  or  if  that  is  impossible,  repetition  of  the  ex- 
periment." We  are  of  the  opinion  that  such  a  sweeping  conclusion 
as  this  is  not  based  upon  sound  and  sufficient  evidence.  The  results 
of  our  studies  considered  in  the  following  pages  are  not  in  harmony 
with  such  a  conclusion. 


'See  Appendix,  page  570. 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  492 

In  fact,  three  experiments  on  swiiije  (76,  jy,  78)  conducted  by 
one  of  the  Canadian  experiment  stations  seem  to  present  evidence 
in  direct  contradiction  to  the  conclusion  of  Wood  and  Stratton. 
These  experiments  involve  i  lot  of  5  pigs,  5  lots  of  6  pigs,  and  4 
lots  of  10  pigs.  The  coefficients  of  variation  of  the  gains  produced 
are  remarkably,  and  with  one  exception,  uniformly  low,  averaging 
only  10.98.  Only  one  of  the  10  lots  possesses  a  coefficient  as  high 
or  higher  than  the  average  for  tlie  experiments  on  swine  performed 
in  this  country,  i.  e.,  17.12.  The  reports  of  these  experiments  are 
too  meager  to  enable  one  to  tell  what  feature  or  features  of  ex- 
perimental control  are  responsible  for  this  low  variability,  but  it 
seems  that  here,  at  least,  a  relatively  high  precision  in  feeding  trials 
has  been  attained  with  only  moderately  large  lots  of  animals. 

(a)    Iiiiportaiicc  of  Reducing  the  Experimental  Error 

The  importance  to  the  technic  of  feeding  experiments  of  some 
method  of  increasing  the  uniformity  of  gains  within  the  lot  as  the 
period  of  observation  increases  should  not  be  underestimated.  The 
difference  between  the  fattening  qualities  of  two  lots  of  animals 
selected  differently,  or  between  two  systems  of  treatment,  is  ex- 
pressed fairly  well  as  "a  percentage  difference  rather  than  a  dif- 
ference of  so  many  pounds  or  ounces.  The  statement  that  Ration  A 
dift'ers  in  fattening  qualities  from  Ration  B  to  the  extent  of  x 
pounds  has  no  meaning  whatever;  the  statement  that  Ration  A 
differs  from  Ration  B  to  the  extent  of  x  pounds  in  3'  days,  or  of 
X  pounds  per  day,  is  perfectly  definite  and  involves  all  necessary 
information ;  but  the  statement  that  Ration  A  is  x  percent  better 
as  regards  fattening  qualities  than  Ration  B  is  less  cumbersome 
and  more  intelligible  than  the  latter  statement,  while  contain- 
ing all  necessary  infomiation.  It  is  a  perfectly  legitimate  as- 
sumption, until  proof  to  the  contrary  is  presented,  that  the 
percentage  difference  between  two  rations  tends  to  remain  con- 
stant thruout  a  feeding  experiment.  Now,  it  may  be  shown  that 
the  smaller  the  coefficient  of  variation  of  the  gains  in  weight  with- 
in a  lot,  other  things  being  equal,  the  smaller  the  minimum  per- 
centage difference  between  the  average  gain  for  the  lot  and  the 
average  gain  for  a  second  lot  that  can  be  definitely  traced  to  the 
difference  in  treatment  or  the  difference  in  make-up  between  the 
two  lots.^  Hence  the  value  of  legitimately  reducing  the  coefficient 
of  variation  of  gains  is  obvious. 

We  will  illustrate  the  point  with  the  data  from  one  of  the 
Rothamsted  experiments  given  in  Table  7,  e.  g.,  the  data  for  the 
lot  of  40  Sussex  wethers.  If  this  experiment  had  closed  at  the 
end  of  4  weeks,  the  final  coefficient  of  variation  of  the  40  total 

"See  Appendix,  pages  571  to  572. 


494  Bulletin  No.  igo  [July, 

gains  in  weight  would  have  been  30.32,  If  another  lot  of  40  Sus- 
sex w^ethers  had  been  under  observation  for  the  same  period  of 
time  and  had  also  exhibited  a  variation  of  30.32  percent,  on  some 
other  ration  we  will  say,  then  the  smallest  difference  in  fattening 
qualities  between  the  two  rations  that  could  be  detected  with  rea- 
sonable certainty  would  be  a  difference  of  12.5  percent;  that  is, 
a  difference  between  the  two  average  lot  gains  of  12.5  percent  is 
the  smallest  difference  that  could  set  up  odds  of  30  to  i  that  the 
difference  in  ration  was  actually  concerned  in  the  difference  in  gain. 
If  this  experiment  had  ended  at  the  end  of  8  weeks,  this  minimal 
difference  between  average  lot  gains  would  have  been  reduced  to 
9.5  percent;  at  the  end  of  12  weeks  it  would  have  been  7.2  per- 
cent; at  the  end  of  16  weeks,  6.2  percent;  and  at  the  end  of  20 
weeks,  5.6  percent.  We  see,  therefore,  that  during  the  course  of 
this  experiment,  which  was  so  conducted  that  the  individual  gains 
were  becoming  more  and  more  uniform,  the  average  lot  gain  be- 
came much  more  efficient  as  a  comparative  value  and  much  more 
representative  of  the  experimental  conditions  whose  influence  on 
the  fattening  of  sheep  it  is  supposed  to  measure. 

To  illustrate  further  the  great  practical  value  of  definite  meth- 
ods of  reducing  experimental  error,  we  will  consider  the  statisti- 
cal data  of  four  experiments  with  poultry  performed  by  F.  T.  Shutt 
of  the  Central  Experiment  Farm,  Canada. 

Experiments  79,  81,  and  82  were  performed  in  1901-02,  and 
Experiment  83  in  1904-05.  As  far  as  the  meager  reports  of  the 
experiments  indicate,  the  feed  in  all  lots  was  given  to  the  fowls  "in 
such  quantity  as  was  immediately  consumed."  In  the  first  three 
experiments,  no  tendency  for  gains  to  become  more  uniform  is 
evident.  In  fact,  in  Experiment  81  the  contrary  tendency  may  be 
seen.  In  Experiment  83,  however,  the  gains  in  each  lot  regularly 
increase  in  uniformity  to  a  very  marked  degree.  The  ration  in 
this  experiment  was  not  very  dift'erent  from  that  of  Experiments 
79  and  81.  In  the  latter,  the  ration  consisted  of  ground  oats,  4 
parts,  ground  barley,  3  parts,  and  meat  meal,  i  part,  made  into  a 
mash  with  skim  milk.  In  the  former,  the  ration  was  ground 
oats,  3  parts,  and  ground  barley,  2  parts,  also  mixed  with  skim 
milk.  It  would  obviously  have  been  to  the  advantage  of  Ex- 
periments 79,  81,  and  82  if  they  had  been  conducted  as  was 
Experiment  83,  tho  just  wherein  Experiment  83  dift'ered  essentially 
from  the  others,  one  cannot  discover  from  the  report.  Perhaps 
the  difference  would  have  been  evident  only  upon  careful  investi- 
gation, for  instance  of  the  quantities  of  feed  consumed  during  each 
week  of  the  experiment. 

The  comment  of  Shutt  upon  the  variability  of  the  gains  ob- 
ser\-ed  in  his  several  lots  of  fowls  is  of  interest:  "What  we  may 
term  individualism  is  as  strone  amone  fowls  as  in  other  classes 


I9i3] 


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Uncertaixty  IX  Interpretation  of  Feeding  Experiments 


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496  Bulletin  No.  165  [July, 

of  live  stock.  Vitality,  constitutional  vigor,  and  ability  to  digest 
and  assimilate  food  are  not  rneted  out  alike  to  all,  and  tho  there 
is  no  apparent  cause,  lack  of  thrift  is  not  uncommonly  to  be  ob- 
served in  some  members  of  a  hatch."  This  belief,  which  is  strik- 
ingly confirmed  by  the  statistical  study  we  have  made  of  some  of 
Shutt's  experiments,  is  undoubtedly  at  the  basis  of  the  general 
practice  of  the  chemistry  and  poultry  divisions  of  the  Central  Ex- 
perimental Farm,  of  presenting  individual  data  in  all  feeding  ex- 
periments on  fowls  and  in  all  experiments  to  determine  the  effect 
of  different  methods  of  poultry  management  on  egg  production. 
It  is  to  be  regretted  that  this  practice  is  so  unusual  among  investi- 
gators of  the  problems  of  poultry  management,  since  it  has  so  much 
in  its  favor  in  rendering  the  results  of  experiments  more  intelligi- 
ble and  less  ambiguous. 

(b)     Selection  of  Anhnals  as  Regards  Age,  Breed  and  Type,  Sex, 
and  Previous  Treatment 

In  securing  the  greatest  possible  uniformity  of  gains  within  the 
lot  in  feeding  experiments,  obviously  the  first  care  should  be  in  the 
selection  of  the  animals. 

Age. — That  animals  at  different  ages  exhibit  different  fattening 
qualities,  needs  no  demonstration,  and  the  necessity  of  including 
only  animals  of  approximately  the  same  age  in  an  experimental  lot 
is   pretty  generally  recognized. 

Breed  and  Type. — That  different  breeds  of  the  same  species  of 
animals  behave  differently  on  the  same  rations  is  undisputed  in 
some  cases,  while  in  all  cases  it  is  a  possibility,  if  not  a  probability, 
in  the  absence  of  definite  evidence  to  the  contrary.  These  dif- 
ferences are  to  be  expected  more  especially  when  the  breeds  differ 
in  general  type.  Thus,  in  the  case  of  steers,  the  dairy  and  beef 
types,  in  the  case  of  swine,  the  lard  and  bacon  types,  and  in  the 
case  of  sheep,  the  mutton  and  wool  types,  may  be  supposed  to  differ 
most  markedly  in  fattening  qualities. 

In  the  case  of  sheep,  the  extensive  breed  tests  conducted  at  the 
Iowa  Station  by  \\'ilson  and  Curtiss^  and  the  extensive  experiments 
of  J.  B.  Lawes  at  Rothamsted  (27,  28,  29)  leave  no  doubt  that 
breed  differences  as  regards  rate  of  growth  do  exist. 

In  the  case  of  steers,  the  evidence  for  the  existence  of  breed 
difference  is  apparently  not  so  convincing,  or  at  least  not  so  gen- 
erally recognized.  Thus,  W.  A.  Henry  says :  "So  far  as  the  data 
go,  we  have  no  evidence  that  beef-bred  animals  make  more  rapid 
growth  than  do  others."^     H.  P.  Armsby  is  inclined  to  the  same 

"Iowa  Agr.  Exp.  Sta.,  Ruls.  33  and  35. 
"Feeds  and  Feeding,  nth  ed.,  1011,  p.  320. 


/p/j]-  U.\ CERTAINTY    IN    INTERPRETATION    OF    FEEDING    EXPERIMENTS  497 

opinion.^  ^^'hile  we  have  not  made  an  extensive  study  of  the  lit- 
erature, some  experiments  that  we  have  reviewed  indicate  in  no 
uncertain  fashion  that  different  breeds,  especially  when  of  differ- 
ent types,  may  exhibit  different  fattening  qualities  under  the  same 
conditions.  An  extensive  experiment  by  H.  \\'.  Mumford  of  this 
station^  presents  indisputable  evidence  to  this  effect.  The  object  of 
the  investigation  was  a  comparison  of  the  six  standard  grades  of 
feeding  steers  as  regards  their  fattening  qualities.  Each  lot  con- 
sisted of  i6  steers  of  the  same  grade.  A  very  complete  description 
of  the  lots  is  given  in  the  original  bulletin.  However,  we  shall  give 
only  a  brief  resume,  more  especially  of  the  characteristics  of  the 
lots  as  regards  their  breeding. 

Of  Lot  I,  containing  the  fancy  selected  feeders,  Mumford  says: 
"They  contained  nearly  loo  percent  of  the  blood  of  the  improved 
beef  breeds.  The  dams  were  high-grade  Shorthorn  cows  and  the 
sire  a  registered  Hereford."  Lot  2,  containing  choice  feeders,  were 
high-grade  Shorthorns.  In  Lot  3,  containing  the  good  feeders, 
beef  blood  still  predominated.  Concerning  Lot  4,  the  medium 
feeders,  the  author  says :  "It  should  be  said  that  this  lot  did  not 
contain  a  steer  that  failed  to  show  evidence  of  improved  beef  blood, 
altho  the  predominating  blood  seemed  to  be  native  or  unimproved, 
with  occasionally  a  dash  of  the  blood  of  some  one  of  the  dairy 
breeds."  Lot  5,  the  common  feeders,  "showed  but  a  ver}-  small 
percentage  of  beef  blood.  Xative  and  unimproved  blood  predomi- 
nated." Lot  6,  the  inferior  feeders,  "showed  no  evidences  of  beef 
blood  and  every  evidence  of  being  scrubs." 

During  a  feeding  period  of  179  days,  these  lots  exhibited  the 
following  average  daily  gains  in  weight :  Lot  i,  2.570  lbs. ;  Lot  2, 
2.543  lbs.;  Lot  3,  2.341  lbs.;  Lot  4,  2.128  lbs.;  Lot  5,  2.207  lbs.; 
and  Lot  6,  1.950  lbs.  While  complete  individual  data  are  not  given, 
thus  precluding  a  complete  analysis  of  the  significance  of  average 
lot  differences,  there  can  be  no  reasonable  doubt,  from  a  study  of 
these  averages,  that  the  infusion  of  beef  blood  tended  strongly  to 
accelerate  the  rate  of  gain  of  the  better  grade  steers. 

While  the  data  of  the  above  experiment  indicate  that  breeds  of 
different  general  types  may  dift'er  in  fattening  qualities,  some  data 
presented  by  Curtiss  before  the  Ames  Graduate  School  during 
the  summer  session  of  1910,*^  indicate  that  decided,  tho  slight,  dif- 
ferences in  rapidity  of  gains  exist  even  among  breeds  of  the  general 
beef  type. 

•U.  S.  Dept.  Agr..  Bur.  An.  Ind..  Bui.  lOS.  pp.  29  and  44.     1908. 

"III.  Agr.  Exp.  Sta.,  Bui.  90. 

'See  E.  Harrison  and  J.  A.  S.  Watson  :  "Correlations  between  Conforma- 
tion and  the  Production  of  Beef  in  Beef  Cattle,  etc."  Thesis  for  the  M.S. 
degree,  Iowa  State  College,  1911. 


\9S 


Bulletin  No.  165 


[July, 


In  the  case  of  swine,  the  evidence  is  unmistakable  that  at 
least  some  breeds  can  be  differentiated  from  each  other  as  regards 
fattening  qualities.  Here  again  breed  differences  are  the  more 
marked  when  accompanied  by  differences  in  general  type.  Appar- 
ently these  differences  are  not  at  all  constant,  but  vary  with  the 
rations  fed  or  with  the  conditions  of  feeding;  that  is,  in  some  ex- 
periments one  breed  may  show  a  marked  superiority  over  another, 
while  in  another  experiment,  in  which  other  rations  are  used  or 
other  conditions  obtain,  the  relation  found  in  the  first  case  may 
be  reversed.  As  an  illustration  of  this  point,  we  shall  first  cite  an 
experiment  by  W.  A.  Henry  of  the  Wisconsin  Station  on  two  lots 
of  12  pigs  each.^  The  total  gains  made  by  the  individual  pigs 
at  the  end  of  12  weeks  on  a  ration  of  corn  and  wheat  middlings, 
and  the  breed  and  sex  to  which  each  pig  belonged,  are  summarized 
in  Table  3. 


Table  3. — Total  Gains  in  Weight  of  Two  Lots  of  Pigs,  with  Breed  and  Sex 

OF  Individuals 


No. 
of 

Lot  I 

Lot   II 

pig 

Breed 

Sex 

Gain 
92 

Breed 

Sex 
barrow 

Gain 

1 

Grade  Berkshire 

barrow 

Grade  Berkshire 

133 

2 

Grade  Berkshire 

sow 

77 

Grade  Berkshire 

sow 

95 

3 

Poland-China 

barrow 

29 

Poland-China 

sow 

55 

4 

Grade  Berkshire 

sow 

103 

Grade  Berkshire 

barrow 

98 

5 

Berkshire 

barrow 

60 

Poland-China 

barrow 

64 

6 

Grade  Berkshire 

barrow 

80 

Grade  Berkshire 

sow    ' 

113 

7 

Yorkshire 

sow 

80 

Poland-China 

barrow 

30 

8 

Berk,   razorback 

sow 

71 

Pol.-Chin.    raz'b. 

sow 

98 

9 

Pol.-Chin.  raz'b. 

barrow 

84 

Berk,  razorback 

sow 

75 

10 

Berkshire 

sow 

87 

Yorkshire 

sow 

81 

11 

Poland-China 

sow 

71 

Berk,    razorback 

barrow 

109 

12 

Poland-China 

barrow 

59. 

Berkshire 

sow 

87 

It  will  be  noticed,  especially  in  the  case  of  Lot  II,  that  the  Po- 
land-China pigs  did  very  poorly.  As  Henry  says :  "The  Poland- 
China  hogs  proved  unsatisfactory  feeders,  showing  losses  at  the 
weighing  period  on  several  occasions.  Towards  the  last  they  be- 
came lame  and  their  conditions  may  be  characterized  as  'broken 
down.'  As  they  had  received  the  same  treatment  at  all  times  as  the 
others,  we  cannot  offer  any  explanation  excepting  that  they  were 
weaker  animals  generally." 

An  Iowa  experiment  on  the  feeding  of  corn  and  supplementary 
feeds  to  pigs  (65)  affords  data  concerning  the  differential  fatten- 
ing qualities  of  different  breeds  of  pigs.  Each  lot  consisted  of  9 
or  10  pigs  and  of  representatives  of  4  or  5  breeds.    The  gains  of  the 

"18th  Annual  Report  of  the  Wisconsin  Station.     1901. 


I9I3] 


UXCERTAIXTV    IX    IXTERPRETATIOX    OF    FeEDIXG    ExPERIMEXTS 


499 


pigs  of  the  various  breeds  as  regards  their  position  above  or  below 
the  mean  gain  of  their  respective  lots  are  given  in  Table  4. 

The  data  in  this  table  are  of  interest,  not  so  much  by  reason  of 
what  thev  prove  as  regards  the  relative  fattening  qualities  of  dif- 
ferent breeds  of  swine,  but  by  reason  of  what  they  suggest.     In 

Table  4. — Data  Coxcerxixg  the  Gaixs  ix  Weight  of  Tex"  Lots  of  Pigs  axd 
Their  Relatiox  to  the  Breed  of  the  Pigs 


Average 
No.  of        gain  for            Lot   ration 
lot                lot 

Pigs  giving  gains 
above  the  respect- 
ive lot  average 

Pigs  giving  gains 
belozc  the  respect- 
ive lot  average 

I 

103.4        Corn  meal. 

timothy  pasture 

3  York-Durocs 

1  Poland-China 

2  Berkshires 
1  Yorkshire 

1  Poland-China 

2  Berkshires 

II 

123.5        Corn  meal  2  pts., 
shorts           1  pt.. 
timothy  pasture 

2  York-Durocs 

1  Poland-China 

2  Berkshires 
1  Yorkshire 

1  York-Duroc 

2  Poland-Chinas 
1  Berkshire 

III           133.2        Corn  meal  1  pt., 
shorts           1  pt., 
timothy  pasture 

1  York-Duroc 
1  Berkshire 
3  Poland-Chinas 
I  Yorkshire 

2  York-Durocs 
2  Berkshires 

IV 

140.9        Corn  meal  3  pts., 
meat  meal  1  pt.. 
timothy  pasture 

1 

3  York-Durocs 
2  Poland-Chinas 
1  Yorkshire 

3  Berkshires 

V           133.9        Corn  meal  5  pts., 
tankage        1  pt.. 
timothy  pasture 

2  York-Durocs 
2  Poland-Chinas 
1  Yorkshire 

1  York-Duroc 
1  Poland-China 

3  Berkshires 

VI 

133.7        Corn   meal, 

clover  pasture 

3  York-Durocs 

1  Poland-China 

2  Berkshires 
1  Yorkshire 

1  York-Duroc 
1  Poland-China 
1  Berkshire 

VII 

90.9        Corn  meal  2  pts., 
shorts           1  pt., 
in   dry  lot 

1  York-Duroc 

1  Poland-China 

2  Berkshires 

2  York-Durocs 

1  Poland-China 

2  Berkshires 
1  Yorkshire 

VIII 

100.2        Corn  meal     1  pt., 
shorts             1  pt, 
in    dry   lot 

1  Poland-China 
1  Berkshire 
3  York-Durocs 

1  Poland-China 
3  Berkshires 

1  Yorkshire 

IX 

121.8 

Corn  meal  5  pts., 
meat  meal  1  pt., 
in   dry  lot 

2  York-Durocs 
2  Poland-Chinas 

1  York-Duroc 

3  Berkshires 
1  Yorkshire 
1  Tamworth 

X            102..')        Corn  meal  ■>  pts.. 
tankage        1  pt.. 
in    dry   lot 

3  York-Durocs 
3  Poland-Chinas 
1  Tamworth 

3  Berkshires 
1  Yorkshire 

500 


Bulletin  No.  165 


[July, 


some  cases  the  suggestion  is  accompanied  by  a  considerable  prob- 
ability, tho  with  such  few  and  heterogeneous  data  that  whatever 
interpretation  is  attempted  must  be  couched  in  very  moderate  lan- 
guage. 

It  will  be  noticed  that  each  lot  contained  a  Yorkshire  pig.  In 
the  first  six  lots,  the  Yorkshire  pigs  exhibit  gains  above,  and  gen- 
erally considerably  above,  their  respective  lot  averages.  In' the  last 
four  lots,  however,  the  Yorkshire  pigs  exhibit  gains  far  below  their 
respective  lot  averages.  It  will  be  noticed  that  the  first  six  lots 
were  turned  out  on  pasture,  while  the  last  four  lots  were  confined 
in  dry  lots.  The  evidence  is  very  suggestive,  therefore,  that  the 
advantage  of  pasture  over  dry  lot  is  much  more  marked  in  the  case 
of  Yorkshire  pigs,  as  representatives  of  the  bacon  type  perhaps, 
than  in  the  case  of  the  other  breeds  experimented  upon. 

It  will  also  be  noticed  that  the  Berkshire  pigs  exhibit  gains 
both  above  and  below  the  average  in  Lots  I,  II,  III,  VI,  VII,  and 
VIII.  In  Lots  IV,  V,  IX,  and  X,  however,  the  Berkshires  con- 
sistently show  gains  below  the  average,  and,  as  the  original  data 
indicate,  far  below  the  average ;  in  short,  the  Berkshire  gains  in 
Lots  IV,  IX,  and  X  are  the  lowest  gains  in  the  lots,  and  in  Lot  V, 
the  three  Berkshires  exhibit  the  two  lowest  and  the  fourth  lowest 
gains  in  the  lot.  These;  four  lots  are  the  lots  in  wiiich  the  corn 
meal  was  supplemented  by  meat  meal  and  tankage,  two  of  the 
lots  being  turned  out  on  pasture  and  two  being  confined  in  dry 
lots.  The  behavior  of  the  Berkshire  pigs  seems  to  be  specific  and 
to  distinguish  these  representatives  of  the  Berkshire  breed  sharply 
from  the  representatives  of  the  other  breeds. 

An  extensive  breed  test  on  swine,  extending  over  three  years, 
was.  conducted  at  the  Iowa  station  by  Curtiss  and  Craig.'"  The 
rations  in  the  three  experiments  differed  to  a  greater  or  less  ex- 
tent. A  summary  of  the  results  obtained  after  the  pigs  were 
weaned  is  given  in  Table  5. 

Table  5. — Breed  Test  at  the  Iowa  Experiment  Station 


I 


I 

] 


First  experiment :    92  days 


Breed 


Ay. 
daily 
Rain 


10  Duroc-Jerseys 

6  Yorkshires 

7  Tamworths 

10  Chester-Whites 
7  Crossbreds 
r^  Poland-Chinas 

10  Berkshires 


.90 
.80 
.77 
.74 
.73 
.72 
.RS 


Second  experiment :    153  days 


Breed 


Av. 
daily 
gain 


9  Yorkshires 
9  Duroc-Jerseys 
10  Berkshires 
10  Chester-Whites 
10  Tamworths 
8  Poland-Chinas 


16 
10 
03 
01 
00 


1.00 


Third  experiment:    165  days 


Breed 


I' 


5  Yorkshires 
10  Berkshires 

8  Tamworths 

10  Poland-Chinas 
10  Duroc-Jerseys 

9  Chester-Whites 


dail 

^- 
1.16 

•■| 

.91 


"Iowa  Agr.  Exp.  Sta.,  Bui.  48.     1900. 


ip-fj] 


Uncektaintv  in   Inteki'Retatiun  ok  Feeding  Experiments 


501 


The  rank  of  the  different  breeds  as  regards  average  daily  gain 
IS  quite  different  in  the  three  experiments,  possibly  because  of  the 
different  rations  used.  The  experiments  agree,  however,  in  several 
particulars,  e.  y.,  in  attributing  to  the  Yorkshire  breed  a  general 
superiority,  and  to  the  Chester-White  and  Poland-China  breeds  a 
general  inferiority.  It  may  be  shown  that  with  a  variability  in  the 
Duroc-Jersey  and  Berkshire  lots  as  high  as  33  percent,  the  odds 
are  30  to  i  that  the  former  breed  possesses  greater  fattening 
.powers  than  the  latter  under  the  particular  conditions  that  obtained 
in  the  first  experiment. 

For  other  experimental  data  on  breed  tests  with  swine,  the 
reader  is  referred  to  Bulletin  47  of  the  U.  S.  Dept.  of  Agr.,  Bu- 
reau of  Animal  Industry,  by  Rommel. 

As  further  evidence  on  the  question  under  discussion,  we  wish 
to  cite  a  few  experiments  in  which  each  lot  consists  of  a  separate 
litter.  Some  statistical  data  on  these  experiments  are  given  in  Ta- 
ble 6. 

Table-  G. — Vartatiti.ity  of  Gains  for  Lots  of  Pigs,  Each  Lot  Consisting  of  a 

Single  Litter 


Reference 


No.  of 

pigs  in 

litter 


Length 

of  exper- 

ment  in 

days 


Statistical 


data  of   total 
in   weight 


gains 


Mean 


Standard 
deviation 


C 


oefficient 

of 
ariation 


"Pigs  observed  from  birth. 
""Pigs  observed  from  weaning 


Wis.  7th  Ann.  Rpt.^' 

7 

119 

64.33 

7.09 

11.02 

8 

119 

86.74 

13.73 

15.83 

7 

119 

70.91 

9.43 

13.30 

7 

119 

65 .  06 

6.69 

10.29 

Mich.    Bui.    138" 

8 

119 

104.60 

9.77 

9.34 

9 

119 

83.55 

4.11 

4.92 

Wis.    Bui.    104" 

10 

56 

53.3 

6.25 

11.73 

10 

56 

24.0 

4.58 

19.08 

5 

.56 

37.6 

3.44 

9.15 

6 

56 

45.3 

7.25 

16.00 

8 

56 

50.5 

8.56 

16.95 

9 

56 

33.0 

6.32 

19.15 

7 

56 

51.3 

5.00 

9.75 

6 

56 

38.0 

2.77 

7.30 

8 

56 

46.0 

6.76 

14.70 

5 

56 

49.2 

7.11 

14.45 

5 

56 

31.4 

6.25 

19.90 

.1 

56 

57.6 

6.67 

11.58 

Total     .  ■. 

130 

Average    

13.00 

time. 


The  coefficients  of  variation  of  the  gains  made  by  these  18  lit- 
ters are  in  general  comparati^•ely  low.  In  only  3  litters  is  the 
coefficient  of  variation  greater  than  the  average  coefficient  for  pigs 


502  Bulletin  No.  165  [July, 

as  indicated  by  the  American  feeding  experiments  reviewed,  i.  e., 
17.12.  It  is  interesting  to  note,  in  view  of  what  has  been  said 
al)ove  as  regards  the  relation  between  the  size  of  gains  and  their 
variabihty,  that  the  three  Htters  exhibiting  the  three  highest  co- 
efficients of  variation  of  the  18  coefficients  exhibit  also  the  three 
lowest  average  lot  gains  obtained  in  the  Wisconsin  experiment. 
The  average  coefficient  of  variation  for  the  18  litters  is  more  than 
4  percent  lower  than  the  general  average  for  American  swine  ex- 
periments, indicating  with  a  high  degree  of  probability  the  ad- 
vantageous effect  of  the  rigorous  selection  of  experimental  animals 
as  regards  breed,  type,  age,  and  ancestry. 

As  regards  the  relative  fattening  qualities  of  the  different  breeds 
of  poultry,  we  shall  simply  refer  the  reader  to  an  extensive  investi- 
gation of  this  question  conducted  at  the  Central  Experimental 
Farm  and  reported  by  Frank  T.  Shutt.^  Nine  different  breeds  were 
under  investigation,  and  while  some  were  quite  similar  in  fattening 
qualities,  some  were  either  markedly  superior  or  markedly  inferior 
to  others. 

It  is  difficult  to  reconcile  such  unequivocal  evidence  as  ap- 
pears to  exist  as  regards  the  differential  fattening  qualities  of  dif- 
ferent breeds  of  animals  with  the  cautious  statements  often  made 
by  authorities  on  the  fattening  of  farm  animals.  We  believe  the 
explanation  lies  in  the  method  ordinarily  used  in  collecting  data 
for  the  solution  of  the  question.  The  ordinary  method  of  solving 
the  question  of  whether  breed  is  a  factor  in  determining  the  rate 
of  growth  is  open  to  considerable  objection.  The  indiscriminate 
averaging  together  of  a  large  niunber  of  experiments  cannot  be 
expected  to  bring  out  any  differential  effect  of  breed.  It  may,  in 
fact,  actually  obscure  all  such  effects,  since  it  is  highly  probable 
(in  some  cases  actually  demonstrated)  that  the  effect  of  breed  on 
growth  and  fattening  is  a  function  of  the  ration  fed  as  well  as  of 
other  experimental  conditions.  The  Kansas  Station  has  shown, 
for  instance,  that  scrub  or  native  steers  do  much  better  than  Short- 
horn steers  when  turned  out  on  poor  pasture,  because  of  their  bet- 
ter foraging  ability,  which  is  a  distinctive  characteristic  of  the 
unimproved  cattle  of  Kansas;  whereas,  in  the  fattening  pen,  the 
Shorthorn  steers  possess  a  more  or  less  distinct  advantage.''  Simi- 
larly, the  typical  bacon  hog  ordinarily  has  the  advantage  over  the 
lard  hog  when  turned  out  on  pasture,  while  when  fed  in  dry  lot 
his  more  restless  temperament  and  his  ability  to  get  around  better 
put  him  at  a  disadvantage.  An  interesting  illustration  of  this  fact 
is  the  behavior  of  the  Yorkshire  pigs  in  the  Iowa  experiment  dis- 
cussed above  (page  500).    Therefore,  the  averaging  of  the  results 

"Canadian  Experimental  Farms,  Report  for  lOOf?,    np.  210-222. 
"Kan.  Agr.  Exp.  Sta.,  Bui.  51.     1895. 


iy;j]  Uncektainty  in  Interpretation  of  Feeding  Experiments  502 

of  experiments  in  which  the  conditions  are  not  strictly  comparable 
tends  to  obscure  any  effect  of  breed,  some  experiments  com- 
pensating for  the  advantage  or  disadvantage  given  to  certain  breeds 
by  other  experiments.  The  best  method  of  attacking  the  problem, 
therefore,  is  the  detailed  study  of  individual  experiments. 

It  may  be  concluded  on  first  thought  that  while  different  breeds 
may  react  differently  to  any  given  ration,  the  disadvantage  accru- 
ing from  this  fact  may  be  counteracted  by  balancing  lots  carefully, 
i.e.,  by  including  the  same  number  of  each  breed  in  each  lot.  Fur- 
thermore, it  seems  to  be  the  opinion  of  some  that  by  including  dif-. 
ferent  breeds  in  the  same  lot  the  experiment  acquires  a  more 
general  significance  and  the  conclusions  of  the  experiment  have  a 
more  general  application.  As  a  matter  of  fact,  as  we  shall  show, 
this  greater  generality  does  not  at  all  result  from  a  loose  selection 
of  animals.  Such  selection  simply  renders  the  results  of  the  ex- 
periment more  ambiguous. 

In  demonstrating  this  fact,  we  shall  first  consider  an  experiment 
by  Henry  of  the  Wisconsin  Station  on  2  lots  of  12  pigs  each,  the 
data  of  which  are  given  in  Table  3.  The  pigs  of  Lot  II  gained,  on 
an  average  per  head,  over  22  lbs.  more  than  the  pigs  of  Lot  I.  It 
may  be  supposed,  on  first  thought,  that  the  conclusion  that  corn 
meal,  which  was  fed  to  Lot  II,  is  better  for  fattening  swnne  than 
whole  corn,  which  was  fed  to  Lot  I,  applies  to  all  the  breeds  of 
pigs  experimented  upon,  i.  c,  grade  Berkshires,  Poland-Chinas, 
Berkshires,  Berkshire  razorbacks,  Poland-China  razorbacks,  and 
Yorkshires.  An  analysis  of  the  individual  data  reveals  a  very  dif- 
ferent state  of  affairs.  The  four  grade  Berkshires  of  Lot  I  gained, 
on  an  average,  86.5  lbs.,  and  the  four  grade  Berkshires  of  Lot  II, 
109.8  lbs.;  the  three  Poland-Chinas  of  Lot  I  gained  53.0  lbs.,  on 
an  average,  while  those  of  Lot  II  gained  only  49.7  lbs. ;  the  two 
Berkshires  of  Lot  I  gained  60  and  87  lbs.  respectively,  while  the 
one  Berkshire  of  Lot  II  gained  87  lbs. ;  the  one  Berkshire  razor- 
back  of  Lot  I  gained  71  lbs.,  and  the  two  pigs  of  the  same  breeding 
in  Lot  II  gained  75  and  109  lbs.,  respectively;  the  Yorkshire  pig 
in  Lot  I  gained  80  lbs.,  and  the  Yorkshire  in  Lot  II,  81  lbs.;  the 
Poland-China  razorback  of  Lot  I  gained  84  lbs.,  and  that  of  Lot  II, 
98  lbs. 

In  summing  up  such  evidence  as  this,  no  certain  conclusion 
applying  to  any  one  breed  of  animals  can  he  deduced.  A  fairly 
high  degree  of  probability  has  been  established  that  for  grade  Berk- 
shires corn  meal  is  better  than  whole  corn,  tho  one  grade  Berk- 
shire in  Lot  I,  fed  v.diole  corn,  gained  more  than  two  in  Lot  II,  fed 
corn  meal.  For  Poland-China  pigs,  however,  the  opposite  conclu- 
sion is  more  applicable.  The  Berkshire  pig  in  Lot  II  exhibited  a 
gain  identical  with  that  of  one  of  the  Berkshires  in  Lot  I.  The 
Yorkshire  in  Lot  II  gained  only  i  lb.  more  than  the  Yorkshire  in 


504  Bulletin  Xo.  1G5  [July, 

Lot  I.  The  Berkshire  razorback  of  Lot  I  gained  only  4  lbs.  less 
than  one  of  the  Berkshire  razorbacks  of  Lot  il,  while  the  difference 
between  the  gains  of  the  two  Poland-China  razorbacks  was  much 
less  than  half  the  ditiference  between  the  gains  exhibited  by  the  two 
Berkshire  razorbacks  of  Lot  II  fed  on  the  same  ration.  Evidently 
the  generality  of  the  conclusion  deduced  from  such  heterogeneous 
experimental  results  has  not  been  extended  in  the  slightest  by  in- 
cluding such  different  breeds  in  the  same  lot.  Only  a  confusing 
ambiguity  has  resulted,  so  that  one  is  not  by  any  means  certain 
that  the  conclusion  applies  to  any  of  the  breeds. 

Many  instances  of  the  marked  disadvantages  of  including  sev- 
eral breeds  in  the  same  lot  may  be  seen  in  the  Iowa  experiment  of 
Kennedy  and  Robbins,  the  data  of  which  are  given  in  Table  4. 
Thus,  consider  Lots  IX  and  X,  the  average  gains  for  which  were 
121. 8  lbs.  and  102.5  lbs.,  respectively.  The  three  Yorkshire-Durocs 
of  Lot  IX  gained  116.7,  122.0,  and  155.0  lbs.,  respectively,  and  the 
three  pigs  of  the  same  breed  in  Lot  X  gained  129.3,  108.3,  ^"d 
123.0  lbs.  It  would  be  difficult  indeed  to  differentiate  these  two 
lots  of  Yorkshire-Duroc  pigs.  The  two  Poland-Chinas  of  Lot  IX 
gained  152.7  and  125.7  lbs.,  while  the  two  Poland-Chinas  of  Lot 
X  gained  165.0  and  140.0  lbs.  Here  also  differentiation  is  impos- 
sible. The  Berkshires  of  Lot  IX  made  gains  of  113.7,  101.7,  and 
lOi.o  lbs.,  and  the  Berkshires  of  Lot  X  made  gains  of  35.0,  26.7, 
and  61.7  lbs.  Apparently  with  this  breed  there  is  a  sharp  differen- 
tiation between  lots.  The  Yorkshire  pig  of  Lot  IX  gained  107.7  lbs., 
and  the  Yorkshire  of  Lot  X,  64.3  lbs.  The  Tamworth  of  Lot  IX 
gained  12 1.7  lbs.,  and  the  Tamworth  of  Lot  X,  171.7  lbs.  On  such 
detailed  analysis  of  Lots  IX  and  X  as  the  above,  the  avoidable  am- 
biguity due  to  differential  breed  characteristics  is  plainly  revealed. 

We.  are  firmly  of  the  opinion  that  froDi  every  standpoint  the 
inclusion  of  different  breeds  and  types  in  the  same  lot  of  experi- 
mental animals  is  a  had  practice,  possessing  no  redeeming  feature. 

Sex. — The  evidence  concerning  the  effect  of  sex  on  fattening 
qualities  seems  to  indicate  quite  clearly  that  the  castrated  male  gains 
faster  than  the  female  of  the  same  species  and  breed. 

In  the  case  of  sheep,  the  evidence  for  this  statement  is  very 
convincing.  Carmichaer  found  in  3  lots  of  sheep,  each  containing 
22  wethers  and  22  ewes,  that  the  wethers,  on  an  average,  made  10 
percent  greater  gains  than  the  ewes.  Thus,  the  average  daily  gains 
at  the  end  of  117  days  were  0.218  and  0.233  lb.  for  the  ewes  and 
wethers,  respectively,  of  Lot  I;  0.210  and  0.231  lb.  for  the  ewes 
and  wethers  of  Lot  II;  and  0.212  and  0.239  lb.  for  the  ewes  and 
wethers  of  Lot  IV.     Curtiss  and  Wilson^  found  the  average  daily 

■Ohio  Agr.  Exp.  Sta.,  Bui.  1S7.     1907. 
"Iowa  Agr.  Exp.  Sta..  Bui.  35.     1897. 


I 


^9^3]  Uncertainty  in  Interpretation  of  Feeding  Experiments  505 


t> 


gains  for  a  lot  of  9  Shropshire  wethers  during  a  feeding  period  of 
106  days  to  be  as  follows:  0.43  lb.  from  September  16  to  30, 
0.44  lb.  for  October,  0.30  lb.  for  November,  and  0.28  lb.  for  De- 
cember. A  lot  of  10  Shropshire  ewes  on  the  same  ration  made  the 
following  average  daily  gains  for  the  same  periods :  0.48,  0.32, 
0.25,  and  0.26  lb.,  respectively.  The  lambs  in  each  lot  were  fed  to 
their  full  capacity  of  the  grain  mixture  used,  and  of  roots  and  hay. 
The  ewe  lambs,  however,  were  the  lighter  eaters.  They  took  on 
fat  rapidly  and  were  more  nearly  finished  during  the  latter  part 
of  the  experiment  than  the  other  lots,  which  consisted  of  wether 
lambs.  According  to  the  authors,  "This  distinction  between  the 
sexes  has  been  observed  in  all  of  the  experiments  made  at  this 
station,  including  both  cattle  and  sheep."  J.  B,  Lawes,  in  an  ex- 
periment covering  a  period  of  140  days  (29),  found  an  average 
gain  of  44.50  lbs.  for  a  lot  of  40  crossbred  wether  lambs,  and  an 
average  gain  of  42.50  lbs.  for  a  lot  of  40  crossbred  ewe  lambs,  the 
breeding  being  the  same.  The  ration  was  oil  meal,  chaffed  clover 
hay,  and  roots,  and  was  fed  to  the  two  lots  in  the  same  quantities 
per  100  lbs.  live  weight.  The  fact  that  the  difference  between  the 
gains  of  ewe  and  of  wether  lambs  in  this  experiment  is  small  is 
probably  due  to  the  method  of  apportioning  the  ration. 

W.  L.  Carlyle,  experimenting  with  two  lots  of  lambs  before  and 
after  weaning  (8),  reports  the  individual  gains.  In  Lot  I,  the 
average  gain  of  the  10  ewes  during  the  10  weeks  before  weaning 
was  33.50  lbs.,  and  that  of  the  7  wethers  during  the  same  period, 
39.12  lbs.  During  the  10  weeks  after  w^eaning,  the  average  gain 
of  the  ewes  was  23.40  lbs.,  and  that  of  the  wethers,  26.86  lbs.  In 
Lot  II,  before  weaning,  the  average  gain  of  the  13  ewes  was  35.70 
lbs.,  and  that  of  the  4  wethers,  40.00  lbs.  After  weaning,  the  aver- 
age gain  of  the  ewes  w^as  22.77  ^^^s.,  and  that  of  the  w^ethers,  16.00 
lbs.  W.  C.  Coffey  (3)  experimented  on  three  lots  of  lambs  of 
different  ages,  there  being  10  lambs  to  the  lot.  The  lambs  were 
under  observation  for  98  days.  In  Lot  I,  the  5  ewes  gained  an 
average  of  25.1  lbs.,  and  the  5  wethers,  an  average  of  31.5  lbs.  In 
Lot  II,  the  6  ewes  gained  an  average  of  25.1  lbs.,  and  the  4  wethers, 
an  average  of  38.4  lbs.  In  Lot  III,  the  5  ewes  gained  an  average 
of  29.5  lbs.,  and  the  5  wethers,  an  average  of  33.7  lbs. 

As  regards  pigs,  the  evidence  on  the  wdiole  favors  the  view 
that  barrows  gain  faster  than  sows  under  the  same  conditions. 
Table  7  contains  data  pertinent  to  the  question  at  issue. 

Carlyle's  experiments  present  contradictory  evidence.  His  lots 
contained  various  breeds  of  pigs.  A  possible  explanation,  there- 
fore, is  that  there  were  more  sows  than  barrows  of  the  breeds  that 
gained  the  faster.  His  experiment,  however,  is  not  reported  in 
sufficient  detail  to  test  the  correctness  of  this  view.  Nevertheless, 
the  table  supports  the  view  that  barrows  are  in  general  better 
gainers  than  sows. 


506 


Bllleti.v  Xo.  105 


[Ji<ly. 


Table  7. — The  Rel.\tive  Fattening  Qualities  of  Barrows  and  Sows 
(All  weights  expressed  in  pounds) 


Refer- 
ence 

No. 


Length  of 

experim'nt 

in  days 


Xo. 

of 

lot 


Barrows 


Sows 


Xo. 


Average 
total  gain 


No. 


Average 
total  gain 


Henry's   Experiments 


59 

84 

10 

117.6 

0 

106.7 

59 

84 

10 

112.3 

9 

112.1 

66 

98 

10 

118.1 

4 

97.5 

66 

98 

7 

147.6 

7 

129.3 

67 

70 

4 

140.2 

5 

134.8 

68 

70 

J 

6 

78.0 

4 

80.0 

68 

70 

5 

113.0 

5 

102.2 

70 

84 

7 

100.5 

5 

100.2 

70 

84 

9 

112.7 

3 

94.7 

71 

84 

4 

115.0 

1 

89.0" 

72 

91 

4 

133.0 

2 

104.5 

72 

91 

4 

158.2 

2 

138.0 

Carlyle's  Experiments 

58 

63 

I 

11                    52. G 

8 

58.0 

58 

63 

n 

12                    43.0 

1 

60.8 

60 

56 

I 

11                     70.4 

10 

71.8 

60 

56 

II 

11                     69.0 

10 

67.6 

Experiment  of  Kennedy  and  Robbins 


65 

112 

I 

5 

99.0 

•5 

107.8 

65 

112 

II 

5 

135.8 

5 

115.0 

65 

112 

III 

5 

137.8 

5 

128.6 

65 

112 

IV 

4 

155.2 

5 

129.4 

65 

112 

V 

5 

161.6 

5 

146.2 

65 

112 

VI 

6 

133.5 

4 

133.5 

65 

112 

VII 

5 

110.6 

5 

71.4 

'    65 

112 

VIII 

5 

102.6 

5 

97.6 

65 

112 

IX 

5 

135.6 

5 

108.4 

65 

112 

X 

6 

103.5 

4 

101.0 

"This  was  the  lowest  gain  in  the  lot. 

That  cockerels  are  much  more  easily  fattened  than  pullets  is  a 
matter  of  common  knowledge  with  poultrymen.  The  experiments 
of  Shutt  (78,  84)  afford  good  e\idence  of  the  correctness  of  this 
statement. 

In  view  of  such  evidence  as  the  above,  indicating  differential 
fattening  qualities  of  the  sexes,  it  is  obviously  bad  practice  to  in- 
clude the  two  in  the  same  experimental  lot. 

Previous  Treatment. — The  differential  effect  of  different  previ- 
ous treatments  of  farm  animals  as  regards  their  fattening  powers 
is  well  known.  For  instance,  given  two  steers  of  the  same  age 
and  breed,  one  of  which  has  been  wintered  on  a  liberal  ration  and 
the  other  on  a  maintenance  ration,  the  latter  will  in  general  take  on 
fat  more  readily  and  economically  than  the  former  in  a  subsequent 
feeding  period.  Therefore,  if  animals  are  selected  for  experi- 
mental purposes  from  different  herds  and  different  localities,  a  pre- 


ip/jl  Uncertainty  in  Interpretation  of  Feeding  Experiments  507 

liminary  feeding-  period  of  considerable  length,  during  which  all 
animals  are  fed  alike,  is  a  wise  precautionary  measure  to  insure  the 
recjuisite  homogeneity  within  lots. 

Conclusion. — There  is  no  advantage  or  necessity  of  introducing 
such  avoidable  factors  of  heterogeneity  as  age,  breed  and  type,  sex, 
and  previous  treatment  into  experimental  lots.  Nothing-  is  gained 
by  so  doing  and  much  is  sacrificed.  The  sources  of  variation,  or 
heterogeneity,  whose  elimination  is  a  veritable  problem,  are  not 
these  gross  factors,  but  the  factors  of  individuality  and  uncontrolled 
experimental  conditions.  The  influence  of  these  factors,  under  the 
best  of  conditions,  is  considerable,  and  to  superimpose  other  variable 
but  avoidable  factors  of  variation  upon  these  is  inexcusable. 

(r)  Changes  in  Variability  of  Gains  Diiring  the  Course  of  a  Feed- 
ing Experiment 

By  a  judicious  selection  of  animals  as  regards  age,  breed  and 
type,  sex,  and  previous  treatment,  tiius  removing  obvious  hetero- 
geneity from  within  the  lot,  the  uniformity  of  individual  experi- 
mental results  will  be  enhanced  in  a  perfectly  legitimate  manner. 
The  question  then  presents  itself  whether  any  changes  occur  in  the 
variability  of  gains  during  the  course  of  a  feeding  experiment  and 
upon  what  these  changes  depend.  \\'e  have  found,  from  a  rather 
extensive  analysis  of  the  results  of  feeding  experiments  in  which 
the  animals  w^ere  weighed  periodically  while  under  observation, 
that  in  some  experiments  the  percentage  variability  of  the  gains 
of  animals  wnthin  the  lot  decreased  more  or  less  regularly  as  the 
experiment  progressed,  while  in  other  experiments  no  such  tend- 
ency was  evident.  It  is  obviously  advantageous  to  decrease 
wherever  possible  and  practicable  the  coefficient  of  variation  of 
gains  in  the  several  experimental  lots,  because  the  smaller  these 
coefficients  the  smaller  is  the  experimental  error  and  the  more  surely 
can  a  given  percentage  difference  between  average  lot  gains  be 
demonstrated  as  causally  connected  with  differences  in  experimen- 
tal conditions." 

Rothamsted  Experiments  with  Sheep. — As  illustrations  of  ex- 
periments in  which  the  percentage  variability  of  individual  gains 
within  the  lot  decreased  as  the  experiment  progressed,  we  shall  first 
cite  the  experiments  of  J.  B.  Lawes  of  the  Rothamsted  Station, 
England  (see  Table  8).  These  experiments  are  peculiarly  suitable 
for  our  purposes,  in  view  of  the  large  lots  of  animals  used  and  the 
care  with  which  the  experimental  conditions  were  controlled. 

A  well-marked  decrease  in  the  percentage  variability  of  the  gains 
in  weight  secured  is  evident  in  each  of  the  above  lots  of  sheep. 
The  feed  for  all  lots  was  of  the  same  description,  namely,  oilcake 
and  chaffed  clover  hay  as  dry  foods,  given  in  fixed  quantities,  and 

'See  formula  on  page  572  of  the  Appendix.    Also  pages  493-496. 


di 


SOS 


Bulletin  No.  165 


[July, 


Table  8. — Ch.\nge  ix  V.\ri.\bility  of  Total  Gains  in  Weight  of  Six  Lots  of 
Sheep,  and  Total  Feed  Consumption  per  Capita  per  Day  for  Succeeding 
Four-Week  Periods 

(All  weights  expressed  in  pounds) 


Total  gain 


Statistical  data  of  total  gains 
in  weight 


Mean 


Standard 
deviation 


Coeffi- 
cient of 
variation 


Average  consumption  of  feed 
per  capita  per  day  for  suc- 
ceeding  4-week  periods 


Oil  cake 


Clover 
hav 


Swedes 


Lot  of  40  Sussex  Wethers   (27) 


In     4  weeks. . . 

10.07 

3.364 

33.40 

.111 

.777 

9.86 

In    8  weeks . . . 

16.82 

4.549 

27.04 

.777 

.777 

9.62 

Li  12  weeks. . . 

22.12 

5.026 

22.72 

.777 

.777 

9.99 

In  16  weeks. . . 

30.32 

5.556 

18.32 

.777 

.777 

10.86 

In  20  weeks. . . 

35.15 

6.910 

19.66 

.777 

.777 

11.00 

In  24  weeks. . . 

46.30 

6.334 

13.68 

1.143 

1.000 

14.13 

In  26  weeks. .  . 

52.72 

7.183 

13.62 

1.143" 

1.000' 

13.64* 

Lot  of  40  Hampshire  Wethers   (27) 


In    4  weeks. .  . 

10.72 

3.9S1 

37.14 

1.000 

1.000 

12.50 

In     8  weeks. . . 

20.35 

4.902 

24.09 

1.000 

1.000 

12.22 

In  12  weeks. . . 

29.90 

6.674 

22.32 

1.000 

1.000 

13.82 

In  16  weeks. . . 

41.02 

8.822 

21.51 

1.000 

1.000 

16.45 

In  20  weeks. . . 

52.59 

10.980 

20.88 

1.000 

1.000 

16.32 

In  24  weeks.. . 

62.79 

10.880 

17.33   ** 

~    1.500 

1.000 

19.30 

In  26  weeks. .  . 

70.12 

10.810 

15.41 

1 . 500' 

1.000' 

16.04' 

Lot  of  46  Cotswold  Wethers  (2S) 


In    4  weeks. . . 

14.46 

3.338 

23.09 

1.000 

1.000 

14.33 

In     8  weeks . . . 

27.15 

5.853 

21.56 

1.000 

1.000 

13.66 

In  12  weeks. . . 

40.57 

7.131 

17.58 

i.oob 

1.000 

17.62 

In  16  weeks. .. 

51.10 

8.421 

16.48 

1.375 

1.000 

16.69 

In  20  weeks^. . 

63.89 

9.990 

15.64 

1 .  393 

.929 

18.58 

Lot 

of  40  Leicester  Weth 

ers  (29) 

In     4  weeks.  . . 

7.50 

3.017 

40.23 

.799 

.799 

10.02 

In     8  weeks. . . 

11.00 

6.012 

54.65 

.799 

.799 

9.23 

In  12  weeks.. . 

23.42 

6.822 

29.13 

.799 

.799 

11.51 

In  16  weeks . .  . 

34.67 

8.329 

24.02 

.799 

.799 

14.29 

In  20  weeks.  .. 

44.57 

9.526 

21.37 

1.000 

.799 

14.80 

Lot  of  40  Crossbred  Wethers  (Sussex-Down  Ewe.  Leicester  Ram)    (29) 


In    4  weeks. . . 

8.75 

2.653 

30.32 

.799 

.799 

9.79 

In    8  weeks. . . 

15.65 

3.575 

22.84 

.799 

.799 

9.08 

In  12  weeks. . . 

25.22 

4.379 

17.36 

.799 

.799 

11.24 

In  16  weeks. . . 

37.20 

5.573 

14 .  98 

.799 

.799 

14.23 

In  20  weeks.  .  . 

44 .  .-)n 

6.052 

13.60 

1.000 

.709 

14.87 

Lot  of  40 

Crossbred 

iiwes  (Sussex-Down 

iwe.  Leicester  Ram) 

(29) 

In    4  weeks. . . 

7.47 

2.976 

39.84 

.750 

.750 

9.47 

In    8  weeks... 

13.22 

3.443 

26.04 

.750 

.750 

8.61 

In  12  weeks.. . 

24.10 

4.188 

17.38 

.750 

.750 

10.87 

In  16  weeks.. . 

34.10 

4.460 

13.08 

.750 

.750 

13.09 

In  20  weeks. .  . 

42.50 

5 .  572 

13.11 

1.000 

.799 

13.69 

'This  is  a  2-week  instead  of  a  4-week  period. 
"Lacking  2  days. 


jp^i] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


509 


swedes  given  ad  libitiiin.  The  dry  foods  were  allotted  according  to 
the  average  initial  weights  of  the  lots,  the  oilcake  being  increased 
by  one-half  toward  the  conclusion  of  the  experiment.  It  will  be 
noted  from  the  table  that  excepting  the  second  4-week  period,  the 
quantities  of  swedes  consumed  increased  in  general  for  all  lots. 

Wohurn  Experiments  with  Sheep. — Another  good  illustration 
of  the  tendency  for  gains  to  become  more  uniform  as  the  experi- 
ment progresses,  is  afforded  by  an  experiment  performed  at  the 
W'oburn  Experimental  Farm,  England,  in  1892,  a  statistical  resume 
of  which  is  given  in  Table  9. 


Table  9. — Change  in  Variability  of  Total  Gains  in  Weight  of  Three  Lots 

OF  Sheep  (23) 

(All  weights  expressed  in  pounds) 


Statistical  data  of  total  gains  in  weight 


Total  gain 


Mean 


Standard 
deviation 


Coefficient 
of  variation 


Lot  L     24  Hampshire  Tegs 


In  36  days. 
In  65  days. 
In  03  da vs. 


19.25 
30.42 
49.25 


3.192 
4.690 
6.050 


16.58 
15.42 
12.28 


Lot  II.     24  Hampshire  Tegs 


In  36  days. 
In  65  da_\s. 
In  93  da vs. 


18.00 
26.42 
41.96 


3.894 
6.204 
7.727 


21.63 
23.48 
18.42 


Lot  III.     24  Hampshire  Tegs 


Jn  36  days. 
In  65  days. 
In  93  davs. 


15.79 
26.33 

43 .  87 


3.807 
4.210 
5 .  652 


24.11 
15.99 
12.88 


At  the  beginning  of  the  experiment,  each  lot  received  3  j  lb.  of 
concentrates  per  head  per  day,  Lot  I  receiving  3^  lb.  of  linseed 
cake.  Lot  II,  ^  lb.  of  linseed  cake  and  34  lb.  of  barley,  and  Lot  III, 
J4  lb.  of  linseed  cake,  1/6  lb.  of  barley,  and  i /12  lb.  of  malt.  At 
the  beginning  of  the  second  period,  the  concentrate  ration  was  in- 
creased to  y^.  lb.,  and  at  the  beginning  of  the  third  period,  to  i  lb. 
Swedes  and  clover-hay  chaff  were  given  ad  libit  it  ni  to  all  lots.  A 
distinct  tendency  for  the  gains  to  become  more  uniform  is  evident. 

A  third-  illustration  of  this  tendency  from  another  experiment 
performed  at  the  Woburn  Station  by  J.  A.  Voelcker,  is  given  in 
Table  10.  The  sheep  used  were  Hampshire-Downs  with  a  slight 
cross  of  Oxford.  The  experiment  started  November  30.  All 
lots  received  at  the  beginning  3/2  lb.  of  linseed  cake  per  head 
daily ;  this  was  increased  on  February  6  to  -34  lb.  All  lots  received 
swedes  or  mangels  ad  libitum,  Lot  I  received  oat-straw  chaff,  and 


510 


Bulletin  No.  165 


U^iy, 


Table  10. — Ch.'WGe  in  Variability  of  Total  Gains  in  Weight  of  Four  Lots 

OF  Sheep  (21) 

(All  weights  expressed  in  pounds) 


Total  gains 


Statistical  data  of  total  gains  in  weight 


}klean 


Standard 
deviation 


Coeffi- 
cient of 
variation 


Mean 


Standard 
deviation 


Coeffi- 
cient of 
variation 


i                Lot  I.     15  Sheep 

Lot  III.     15  Shetp 

In 
In 

50 
98 

days 

days. . .  . 

21.67      1      6.294            29.05 
40.73             5.650             13.87 

24.13      1      4.631      j       19.19 
42.47      '      5.690      '       13.40 

Lot  II.     15  Sheep 

Lot  IV.     15  Sheep 

In 
In 

50 

98 

days. . . . 
days 

21.27             5.893            27.71 
41.67             7.578             18.19 

25.27            3.549             14.04 
44.80            7.608             16.98 

Lot  II,  meadow-hay  chaff,  ad  libitum.  Lot  III  received  oat-straw 
and  meadow-hay  chaff  ad  libitum  in  equal  parts,  well  mixed.  Lot 
IV  received  mixed  grain,  about  Yj,  lb.  per  head  per  day  thruout  the 
experiment.  In  the  words  of  Voelcker,  "There  is  very  little  doubt 
that  the  sheep  would  have  taken  a  considerably  larger  amount  of 
dried  grains  had  they  been  allowed  it,  but  this  could  not  have  been 
economical."  Lot  I  ate  the  most  roots,  Lot  II,  the  next,  and  Lot  IV, 
the  least.  The  latter  lot  was  the  only  one  that  did  not  exhibit  in- 
creasing uniformity  of  gains  as  the  experiment  progressed.  The 
following  statement  in  the  report  of  this  experiment  is  of  inter- 
est: "The  losses  and  inequalities  generally  found  in  feeding  a 
number  of  sheep  during  a  winter  were,  mainly  owing  to  the  very 
open  character  of  the  weather,  very  small." 

loii'a  Bxpcrimcnt  zcith  Pigs. — A  lot  of  24  pigs  in  an  experiment 
at  the  Iowa  Station  carried  out  by  L.  G.  ^Michael  and  W.  J.  Ken- 
nedy (61)  exhibited  gains  which  became  more  and  more  uniform 
as  the  experiment  progressed,  as  the  data  in  Table  1 1  testify. 


Table  11.— Change  in  Variability  of  Total  Gains  in  Weight  of  a  Lot  of 

Twenty-four  Pigs  (61) 

(All  weights  expressed  in  pounds) 


Total  gain 

Statistical  data  of  total  gains  in  weight 

Corn  consumed 
per  head  per 

Mean 

Standard          Coefficient 
deviation        of  variation 

day  for  suc- 
cessive periods 

In  10  davs 

3.46 
15.87 
22 .  58 
.35 .  33 
43 .  57 
40.70 

3.93 
3.54 
4.15 
3.71 
4.00 
4.40 

113.60 

22.31 

18.39 

10.50 

9.18 

8.85 

3  85 

In  20  days 

In  30  days 

In  40  days 

In  48  days  (23  pigs) 
In  55  days  (23  pigs) 

4.84 
4.85 
5.27 
5.22 
5.29 

i9U] 


UnCERT.MXTV    1.\    I.NTEKPKtlWTION    OF    FeEUIXG    EXPERIMENTS 


511 


The  pigs  in  this  experiment  all  received  the  same  amount  of 
feed  thruout  the  experiment,  being  fed  individually.  The  ration 
was  corn  alone  and  corn  supplemented  by  various  stock  foods; 
hence  the  low  gains.  Since  the  stock  foods  apparently  had  no  dif- 
ferential effect  and  did  not  produce  gains  significantly  different 
from  corn  alone,  all  of  the  data  are  treated  together  instead  of  in 
four  lots.  The  corn  ration  was  increased  from  time  to  time  as  the 
experiment  progressed. 

Michigan  Bxperiment  with  Pigs. — G.  D.  Smith  reports  a  feed- 
ing experiment  on  2  lots  of  pigs  under  observation  from  birth.''  On 
an  increasing  ration,  the  variability  of  gains  decreased  during  17 
weeks  of  the  exi>eriment.  The  statistical  data  of  this  investigation 
are  given  in  Table  5  of  the  Appendix.'' 

IllinGis  Bxpcrinicnt  zcith  Steers. — In  Bulletin  103  of  the  Illi- 
nois Station,  H.  W.  Mumford  reports  the  results  of  an  experi- 
ment on  10  lots  of  high-grade  Shorthorn  steers,  the  lots  consisting 
of  10  or  15  steers  each.  The  statistical  data  for  the  first  16  weeks 
and  the  total  22  weeks  are  given  in  Table  12.  In  this  table  it  will 
be  noticed  that  the  average  daily  gain  per  steer,  instead  of  the  aver- 
age total  gain  per  steer,  is  considered.    It  may  be  easily  shown  that 

T.\BLE  12. — Ch.^nce  in  Variability  of  Aver.vge  Daily  Gains  in  Weight  of  Ten 
Lots  OF  Shorthorn  Steers  (43) 

(All  weights  expressed  in  pounds) 


Average 

Statistical  data  of  daily  gains  in  weight 

daily  gain 
per  steer 

Mean 

Standard 
deviation 

Coeffi- 
cient of 
variation 

Mean 

Standard 
deviation 

Coeffi- 
cient of 
variation 

Lot  L     10  Steers 

Lot  IV.     15  Steers 

In  16  weeks. .  . 
In  22  weeks.  . . 

2.481 
2 .  486 

.512 
.  3,54 

20.64 
14.24 

2.321 
2.412 

.473 
.383 

20.38  . 
15.96 

Lot  IT.     15  Steers 

Lot  VII.     15  Steers 

In  16  weeks. .  . 
In  22  weeks..  . 

2.533                .636             25.09 
2.499                .503             20.13 

2.353 
2 .  534 

.524      1      22.27 
.242      1        9.55 

Lot  III.     15  Steers 

Lot  VITI.     10  Steers 

In  16  weeks. . . 
In  22  weeks.  . . 

2.072               .497      \      23.99 
2.181               .415             19.03 

1.072                .350             17.75 
2.106               .200            13.77 

Lot  TV.     15  Steers 

Lot  IX.     10  Steers 

In  16  weeks. . ., 
In  22  weeks.  . . 

2.353       1         .437             18.58 
2.473               .489      1      19.77 

2.026      1         .652 
2.025               .431 

32.18 
21.28 

Lot  V.     15  Steers 

Lot  X.    10  Steers 

In  1 6  weeks . . . 
In  22  weeks.  . . 

2.266               .375      |      16.55 
2.470                .388       '       15.71 

1.920 
1.995 

.640      1      33.33 
.539      '      27.02 

'Mich.  .\gr.  Exp.  Sta..  Riil.  138.     1896. 
''See  page  573. 


512  Bulletin  No.  16j  [J»ly, 

the  coefficient  of  variation  of  gains  reduced  to  the  daily  hasis  is 
the  same  as  the  coetiicient  of  variation  of  the  original  total  gains. 

In  each  lot,  with  the  exception  of  Lot  IV,  the  gains  for  the  22- 
week  period  were  more  uniform  than  the  gains  for  the  16-week 
period.  The  quantities  of  feed  consumed  by  the  lots  were  changed 
as  the  experiment  progressed,  the  concentrates  in  general  being 
increased  and  the  roughages  decreased. 

Canadian  Experiment  iSth  Steers. — At  the  Xappan,  Xova  Sco- 
tia, Station,  R.  Robertson  ran  an  experiment  on  3  lots  of  8  Short- 
horn steers  for  135  days.  The  statistical  data  for  periods  of  15 
days  are  given  in  Table  13. 

In  each  of  the  above  three  lots  of  steers,  it  is  evident  that  there 
was  a  pronounced  tendency  for  the  gains  to  become  more  uniform 
as  the  experiment  progressed.  It  is  of  interest  to  note  that  the  high 
coefficients  for  all  lots  for  the  first  15-day  period  are  probably  con- 
nected with  the  fact  that  in  this  experiment,  contrary  to  ordinary 
practice,  a  preliminary  feeding  period  was  not  included.  All  lots 
were  fed  alike,  as  far  as  possible,  for  the  entire  experiment.  The 
concentrates  in  the  ration  (mixed  meals)  were  regularly  increased 
from  start  to  finish,  while  the  hay  (or  straw)  and  succulent  feeds 
(roots  and  ensilage)  were  decreased. 

Summary  of  the  Bi'idence. — The  experimental  data  presented 
in  Tables  8  to  13  inclusive  are  sufficient  to  show  that  in  some  cases, 
at  least,  feeding  experiments  may  be  so  conducted  that  the  percent- 
age variation  of  gains  within  the  lot  will  decrease  as  the  period  of 
observation  increases.  As  to  whether  this  decrease  would  continue 
indefinitely  or  would  stop  with  some  minimum  coefficient,  the  data 
cited  can  offer  no  conclusive  verdict.  It  is  evident,  however,  that 
the  increase  in  the  uniformity  of  lot  gains  is  ordinarily  the  most 
rapid  in  the  early  periods  of  the  experiment,  while  in  the  closing 
periods  of  the  experiment  in  most  cases  the  change  in  the  coefficient 
of  variation  is  gradual.  In  fact,  in  some  of  the  cases  cited,  the  co- 
efficient was  practically  constrnt  for  the  last  two  or  three  periods. 
From  such  facts  we  are  inclined  to  believe,  therefore,  that  the  co- 
efficient of  variation  of  lot  gains  cannot  be  reduced  beyond  a  cer- 
tain mininmm  characteristic  of  the  experimental  conditions  and  of 
the  sample  of  animals  under  observation. 

((/)  Bffect  of  Change  of  Ration  on  J^ariability  of  Gains 

Illinois  Experiment  icith  Sheep. — Many  of  the  feeding  experi- 
ments whose  results  we  have  submitted  to  a  statistical  analysis 
either  have  failed  utterly  to  exhibit  any  progressive  change  in  the 
coefficient  of  variation  of  gains  within  lots,  or  have  exhibited  only 
slight  reductions,  generally  in  the  fore  part  of  the  experiment.  We 
shall  consider,  first,  in  this  connection,  some  unpublished  data  on 


IQU] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


513 


w 
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o 

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514 


Bulletin  No.  105 


[July. 


lamb  feeding  collected  by  this  station.  Three  lots  of  7  lambs  each 
were  nnder  observation  for  24  weeks.  A  statistical  resume  of  the 
experiment,  as  far  as  the  gains  in  weight  and  the  feed  consumed 
are  concerned,  is  given  in  Table  14. 


fi 


Table  14. — Chance  in  Variability  of  Total  Gains  in  Weight  of  Three  Lots 
OF  Lambs,  and  Total  Feed  Consumption  per  Lot  per  Period" 

(Gains  in  weight  expressed  in  pounds:  feed  consumed  expressed  in  kilograms) 


Total  gain 


Statistical  data  of  total  gains 
in  weight 


Mean 


Standard 
deviation 


Coeffi- 
cient of 
variation 


Total  consumption  of  feed 
per  lot  per  4-week  period 


Alfalfa 
hay 


Corn 
meal 


Oil 
meal 


Lot  I. 

7  Lambs 

In    4  weeks. . . . 

10.93 

2.162 

19.78 

156.4 

82.5 

5.41 

In    8  weeks.  . .  . 

20.00 

2.000 

10.00 

155.5 

96.0 

5.06 

In  12  weeks. . .  . 

29.86 

1.619 

5.42 

144.6 

108.7 

5.72 

In  16  weeks. . . . 

38 .  50 

1.615 

4.19 

125.2 

118.8 

6.25 

In  20  weeks. . .  . 

45.53 

3.963 

8.70 

119.2 

120.4 

6.33 

In  24  weeks. . . . 

,54.00 

3 .  093 

5 .  73 

117.6 

117.2 

6.16 

Lot   II. 

7  Lambs 

In     4  weeks.  . .  . 

13.64 

3 .  248 

23.  SI 

166.7 

66.2 

23 . 5 

In    8  weeks.  ..  . 

22.79 

3 .  853 

16.91 

173.8 

79.1 

26.6 

In  12  weeks.  . .  . 

33.86 

4.307 

12.72 

159.7 

88.8 

29.8 

In  16  weeks. . .  . 

42.29 

6.702 

15.85 

138.3 

97.8 

32.5 

In  20  weeks. .  . . 

49.39 

8.371 

16.95 

119.3 

102.8 

34.3 

In  24  weeks. . . . 

60.50 

9.464 

15.  C4 

124.1 

103.0 

34.3 

Lot  III 

7  Lambs 

In    4  weeks 

1 2 .  79 

1.870 

14.62 

177.3 

48.4 

48.4 

In     8  weeks. .. . 

23 .  29 

2.801 

12.03 

182.6 

56.2 

56.2 

In  12  weeks. . . . 

32.07 

2.692 

8.39 

163.8 

62.3 

62.3 

In  16  weeks. ..  . 

42.93 

2.744 

6.39 

150.9 

68.4 

68.4 

In  20  weeks. ..  . 

50.40 

4.045 

8.03 

139.1 

73.0 

73.0 

In  24  weeks.  . .  . 

0 1  .  .'{6 

3.758 

6.12 

137.0 

72.6 

72.6 

"Unpublished  data  from  the  111.  Agr.  Exp.  Sta.  H.  S.  Grindley.  W.  C. 
Coffev,  and  A.  D.  Emmett,  with  the  co-operation  of  W.  E.  Carroll  and  Sleeter 
Bull. 

It  will  be  noticed  that  in  all  three  lots  a  decrease  in  the  coeffi- 
cient of  variation  occurred  for  the  first  three  or  four  periods  only. 
An  examination  of  the  quantities  of  feed  consumed  per  period  is, 
we  believe,  suggestive  of  an  explanation.  We  have  tabulated  this 
information  in  the  last  three  columns  of  the  table,  the  weights  of 
feeds  being  given  in  kilograms. 

It  will  be  seen  that  the  alfalfa  hay  consumed  in  general  decreased 
for  all  lots  from  the  first  to  the  last  period,  the  most  notable  ex- 
ceptions being  slight  increases  for  Lots  II  and  III  from  the  first  to 
the  second  4-week  periods.  The  corn  meal  and  oil  meal  in  general 
were  increased  rather  steadily  from  the  first  to  the  fourth  period. 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  515 

From  the  fourth  to  the  fifth  period  only  a  shght  increase  in  the 
consumption  of  these  feeds  occurred  in  Lots  I  and  II,  tho  in  Lot 
III  there  was  a  more  marked  increase.  During  the  fifth  and  sixth 
periods  the  consumption  of  all  feeds  was  practically  constant. 

Comparing  these  changes  in  feed  consumption  with  the  cor- 
responding changes  in  the  percentage  variability  of  gains  in  weight, 
one  is  inclined  to  the  opinion  that  an  increasing  feed  consumption 
is  in  general  accompanied  by  an  increasing  uniformity  of  gains 
within  the  lot  as  measured  by  the  coefficient  of  variation,  while  a 
constant  or  decreasing  feed  consumption  is  in  general  accompanied 
by  a  constant  or  decreasing  uniformity  of  gains.  This  conckision 
is  not  incompatible  with  the  experiments  above  cited,  tho  in  the 
latter,  at  times,  a  constant  feed  consumption  was  accompanied  by 
an  increasing  uniformity  of  gains.  Also,  the  conclusion  reached 
above,  that  within  any  experiment  the  lots  making  the  best  gains 
generally  exhil)it  the  most  uniform  gains,  falls  in  line  with  this 
conception,  which  may  be  restated  in  the  proposition  that  conditions 
favorable  to  good  gains  are  also  favorable  to  uniform  gains.  It  is 
probable  that  other  factors  than  change  in  ration  enter  into  the 
([uestion.  Possibly  the  relation  of  the  feed  consumption  to  the 
bodily  requirements  is  also  concerned  in  the  changes  in  variability 
of  the  gains  in  weight,  a  liberal  feed  consumption,  possibly,  being 
conducive  to  an  increasing  uniformity  of  gains.  Other  factors, 
such  as  changes  in  the  weather  conditions,  very  probably  exert  an 
etfect  (see  page  523). 

Wisconsin  Experiments  with  Swine. — We  wish  to  consider 
next  two  experiments  conducted  at  the  Wisconsin  Station  by  W. 
L.  Carlyle  in  1897  and  1898.  The  object  was  to  compare  rape  and 
clover  pasture  for  fattening  swine.  Corn  meal  and  shorts  or  mid- 
dlings were  given  as  supplementary  feeds.  The  average  total  gains, 
standard  deviations,  and  coefficients  of  variation,  as  well  as  the 
total  consumption  of  supplementary  feeds  per  lot  per  period,  are 
given  in  Table  15. 

In  the  experiment  of  1897,  the  consumption  of  corn  meal  and 
shorts  varied  only  within  narrow  limits  for  8  weeks  and  was  the 
same  for  the  two  lots.  However,  in  the  case  of  Lot  I  the  coefficient 
of  variation  decreases  almost  continuously  from  period  to  period, 
while  in  the  case  of  Lot  II  no  consistent  change  is  evident.  In 
kK)king  for  an  explanation  of  this  difference  between  the  two  lots, 
the  description  given  of  the  rape  and  clover  pastures  is  suggestive: 
"The  rape  was  quite  immature  when  the  experiment  began  and  as 
a  consequence  it  steadily  improved  in  quality,  while  the  clover  was 
better  when  the  experiment  began  than  it  was  later."  Apparently, 
for  Lot  I  the  pasturage  w^as  more  palatable  and  was  more  vora- 
ciously eaten  as  the  experiment  progressed,  while  for  Lot  II,  the 


516 


Bulletin  No.  165 


[July. 


Table  15.— Chance  in  Variability  of  Total  Gains  in  Weight  of  Four  Lots 
OF  Pigs,  and  Total  Feed  Consumption  per  Lot  per  Period  (.58,  60) 

(All  weights  expressed  in  pounds.) 


Total    gain 


Statistical  data  of  total  gains 
in   weight 


Mean 


Standard 
deviation 


Coeffi- 
cient  of 
variation 


Feed  consumption 
per   period 


Corn 
meal 


Shorts  or 
middlings 


Lot  I. 

19  Pigs  on  Rape  Pasture   (1S9T 

) 

In  ii   weeks 

12. 2G 

3.242 

26.44 

590 

295 

In  4  weeks 

22.21 

3.915 

17.63 

560 

280 

In  6  weeks 

35.26 

6.640 

18.83 

627 

313 

In  8  weeks 

47.11 

7 .  933 

16.84 

630 

315 

In  9  weeks 

54 .  S9 

8.509 

15.. 50 

315 

157 

Lot  11.     10  Pigs  on  Clover  Pasture   (1897) 


Lot  I.     21   Pigs  on  Rape  Pasture   (1898) 


In  2  weeks 

10.11 

3.837 

37.95 

590 

295 

In  4  weeks 

19.95 

7.937 

39 .  78 

560 

280 

In  6  weeks 

38.05 

10.831 

28.46 

627 

313 

In  8   weeks 

45.47 

14.711 

32 .  35 

630 

315 

In  9   weeks 

49 .  53 

13.885 

28.03 

315 

157 

In  2  weeks 

20.43 

3.320 

16.25 

650 

325 

In  4  weeks 

37.62 

4.402 

11.70 

770 

385 

In  6  weeks 

54.47 

6.751 

12.39 

910 

455 

In   8   weeks 

7 1  .  05 

9.400 

13.23 

980 

490 

Lot  11. 

21  Pigs 

or 

Clover 

Pasture   (1 

808) 

In 

2 

weeks.  . . 

16.52 

2.570 

15.  56 

650 

325 

In 

4 

weeks . . . 

33.43 

5.114 

15.30 

770 

385 

In 

6 

weeks .  . . 

50.48 

6.814 

13.50 

910 

455 

Jn 

8 

weeks.  . . 

68 .  33 

8.800 

12.88 

980 

490 

reverse  was  true ;  for  this  reason,  probably,  there  was  an  increasing 
uniformity  of  gains  in  Lot  I  but  not  in  Lot  IL 

The  experiment  of  1898  affords  an  interesting  confirmation  of 
this  view.  Here  both  lots  received  the  same  quantities  of  corn 
meal  and  middlings,  the  consumption  of  these  concentrates  increas- 
ing as  the  experiment  progressed.  In  this  case,  however,  the  clover- 
pasture  lot  (II)  exhibited  a  regularly  increasing  uniformity  of 
gains,  while  the  rape-pasture  lot,  except  for  an  initial  increase  from 
the  first  to  the  second  period,  exhibited  a  decreasing  uniformity  of 
gains.  Again  referring  to  the  description  of  the  pasturage,  we 
find  that  "When  the  pigs  were  first  put  on  the  rape  it  was  in  prime 
condition  for  them,  whereas  later  it  became  more  ripe  and  woody 
and  they  did  not  relish  nor  eat  it  as  they  did  at  first.  The  clover, 
on  the  contrary,  was  somewhat  parched  and  dry  when  the  experi- 
ment began,  but  grew  very  succulent  and  tender  as  the  fall  rains 
came  on." 

Henry's  Expcr'unoiis  at  Wisconsin  li'itJi  Pigs. — \\'e  shall  cite 
next  several  experiments  perfonned  at  the  \Msconsin  Station  by 
W.  A.  Henry  and  associates.    The  experiments  are  representative  of 


Jp/J] 


Uncert-M-ntv  in   Inteki'Ket.vtio.n  or  Feeding   F.xperiments 


517 


a  series  extending  over  ten  years,  the  purpose  of  which  was  to 
determine  the  vahie  of  whole  corn  as  compared  with  corn  meal  as 
the  main  portion  of  the  ration  for  fattening  pigs.  The  statistical 
data  of  the  first  experiment  which  we  shall  consider  are  given  in 
Table  i6. 


T.ABLE  16. — Change  in  Variability  of  Total  Gains  in  Weight  of  Two  Lots 
OF  Pigs,  and  Total  Feed  Consumption  per  Lot  per  Week  (59) 

(All  weights  expressed  in  pounds) 


Total  gain 


Statistical  data  of  total  gains 
in  weight 


Mean 


Standard 
deviation 


Coeffi- 
cient of 
variation 


Feed  consumption 
per  week 


Corn 


Wheat 
middlings 


Lot  L     19  Pi 

gs  (Whole  Corn) 

lu     1  week 

8.37 
20.05 

2.65 
2.72 

31.66 
13.57 

490 
560 

245 

In     2  weeks 

280 

In     3  weeks 

30.26 

5.24 

17.32 

630 

315 

In     4  weeks 

35.74 

5.31 

14.87 

560 

280 

In     5  weeks 

45.89 

6.77 

14.75 

560 

280 

In     6  weeks 

58.16 

8.74 

15.03 

616 

308 

In     7  weeks 

69.63 

11.88 

17.06 

616 

308 

In     8  weeks 

77.11 

11.28 

14.62 

616 

308 

In     9  weeks 

87.05 

12.26 

14.09 

616 

308 

In   10  weeks 

96.26 

14.82 

15.40 

616 

308 

In   11   weeks 

102.40 

14.38 

14.05 

616 

308 

In    12   weeks 

112.41) 

16.02 

14.25 

588 

294 

Lot  II.     19  Pigs   (Corn  Meal) 


In 
In 
In 
In 
In 
In 
In 
In 
In 
In 
In 
In 


week. . 
weeks, 
weeks, 
weeks, 
weeks . 
weeks, 
weeks. 

8  weeks. 

9  weeks. 

10  weeks. 

11  weeks. 

12  weeks. 


8.37 
19.26 
28.95 
35.16 
44.53 
56.47 
67.37 
76.42 
89.21 
97.16 
101.30 
112.20 


Z.  i.} 

4.41 
4.15 


5.70 
7.01 

8.14 
8.87 
10.63 
10.18 
11.61 
13.99 
14.82 


32 .  90 
22 .  90 
14.33 
16.23 
15.73 
14.41 
13.17 
13.91 
11.41 
11.95 
13.81 
13.21 


490 
560 
630 
560 
560 
616 
616 
616 
644 
644 
644 
616 


245 
280 
315 
280 
280 
308 
308 
308 
322 
322 
322 
308 


In  Lot  I,  from  the  6th  week  to  the  I2tli  the  ration  was  prac- 
tically constant  and  consequently  the  coefficient  of  variation  of  the 
total  gains  in  weight  produced  shows  no  tendency  to  consistently 
decrease  as  the  period  of  observation  increases.  In  fact,  from  the 
2d  to  the  1 2th  week  the  coefficients  vary  within  relatively  narrow 
limits. 

The  coefficients  of  variation  of  gains  in  weight  for  Lot  TI  con- 
form more  closely  to  the  changes  in  the  quantity  of  feed  consumed. 
The  continuous  increase  in  the  latter  during  the  first  3  weeks  is 
associated  with  a  continuous  decrease  in  the  coefficient  of  variation. 


} 


513 


Bulletin   No.   165 


[July. 


The  decrease  in  feeds  during  the  4th  week  produced  an  increase  in 
the  coefficient.  Xo  change  in  feed  during  the  5th  week  accom- 
panied a  shght  decrease  in  the  coefficient.  A  large  increase  in  feed 
intake  at  the  beginning  of  the  6th  week  produced  a  reduction  in 
the  coefficient.  A  constant  intake  for  the  next  two  weeks  was  ac- 
companied by  a  further  decrease  in  the  coefficient,  followed  by  an 
increase.  An  increase  in  feed  intake  at  the  beginning  of  the  9th 
week  occasioned  a  marked  decrease  in  the  coefficient.  The  con- 
stant feed  intake  of  the  next  two  weeks  apparently  effected  first  a 
gradual  increase  and  then  a  marked  increase  in  the  coefficient  of 
variation.  The  decrease  in  feed  intake  at  the  beginning  of  the 
1 2th  week  was  accompanied  by  a  slight  decrease  in  the  coefficient 
of  variation,  this  effect  being  anomalous. 

The  second  experiment  of  this  series,  which  we  have  subjected 
to  a  statistical  study,  gave  the  data  contained  in  Table  17. 

Table  17.— Change  in  Variability  of  Total  Gains  in  Weight  of  Two  Lots 
OF  Pigs,  and  Total  Feed  Consumption  per  Lot  per  Week" 

(All  weights  expressed  in  pounds) 


Total  gain 


Statistical  data  of  total  gains 
in  weight 


Mean 


Standard 
'  deviation 


Coeffi- 
cient  of 
variation 


Total  feed  con- 
sumption per  week 


Corn        Middlings 


Lot  L     12   Pigs   (Whole  Corn) 


In 
In 
In 
In 
In 
In 
In 
In 
In 


week. . 
weeks, 
weeks, 
weeks . 
weeks, 
weeks, 
weeks . 
weeks . 
weeks. 


In  10  weeks. 
In  11  weeks. 
In   12  weeks. 


14.92 
19.67 
28.58 
34.33 
46.67 
49.58 
53.00 
57.58 
62.83 
66.08 
69.33 
74.42 


,19 

.50 
,27 
,44 


6.86 

9.85 

8.20 

9.06 

11.97 

15.42 

16.25 

18.20 


34.70 
22.  SG 
14.94 
15.84 
14.70 
19.87 
15.47 
15.73 
19.05 
23.34 
23.44 
24.45 


2S5 
320 
326 
340 
325 
308 
290 
288 
284 
252 
260 
226 


142 
160 
163 
170 
163 
154 
145 
144 
142 
126 
130 
113 


Lot  II.     12  Pigs   (Corn  Meal) 


In 
In 
In 
In 
In 
In 
In 
In 
In 


In  10 
In  n 
In  12 


week . . 
weeks, 
weeks, 
weeks, 
weeks, 
weeks, 
weeks, 
weeks, 
weeks, 
weeks, 
weeks, 
weeks. 


14.00 

2.45 

17.50 

18.50 

3.55 

19.17 

29.12 

4.40 

15.12 

39.83 

6.22 

15.61 

50.58 

8.67 

17.15 

58.42 

10.50 

17.97 

61.00 

10.93 

17.90 

66.00 

13.63 

20.65 

71.17 

14.27 

20.05 

76.75 

18.18 

23.69 

80.67 

22.21 

27.53 

86.50 

26.71 

30 .  88 

293 
340 
350 
360 
361 
356 
317 
312 
302 
302 
308 
230 


146 
170 
175 
178 
181 
178 
159 
156 
151 
151 
154 
115 


*Wis.  Agr.  Exp.  Sta.,  18th  Annual  Report.     1901. 


1913]  Uncertainty  in  Interpretation  of  Feeding  Experiments  519 

After  an  initial  increase  for  the  first  4  or  5  weeks,  the  ration 
decreased  fairly  regularly  to  the  end  of  the  experiment,  in  both 
lots,  the  increase  in  ration  was  accompanied  by  a  decrease  in  per- 
centage variability  of  gains  in  weight,  while  the  decrease  in  ration 
from  the  4th  or  5th  week  occasioned  an  increase  in  variability  that, 
in  Lot  II  at  least,  became  more  and  more  pronounced  as  the  ex- 
periment progressed,  so  that  in  Lot  I  the  variability  of  the  gains 
for  the  entire  experiment  was  larger  than  the  variability  of  the 
gains  for  the  first  2  weeks,  while  in  Lot  II  the  unique  condition 
of  much  more  variable  gains  at  the  end  than  at  the  beginning  of 
the  experiment,  resulted. 

Four  more  of  the  experiments  01  Henry  and  associates  have 
been  subjected  to  an  analysis  similar  to  the  above.  The  statistical 
data  for  these  are  included  in  Tables  6  to  9,  inclusive,  of  the  Ap- 
pendix.* In  some  of  the  lots  in  these  investigations  the  correlation 
between  change  in  ration  and  change  in  the  percentage  variability 
of  gains  is  very  evident. 

Of  these  experiments,  only  Experiment  32  calls  for  special  com- 
ment. In  this  experiment,  altho  the  ration  increased  more  or  less 
regularly  from  the  beginning  to  the  end,  the  coefficient  of  variation 
of  the  gains  in  weight  of  both  lots  decreased  to  a  minimum  and 
then  abruptly  increased  and  remained  at  the  higher  level  for  the 
rest  of  the  experiment.  It  is  obvious  that  this  is  hardly  to  be  ex- 
pected from  the  experiments  thus  far  reviewed  and  from  the  con- 
clusions we  have  thus  far  developed  of  the  effect  of  change  of  ration 
upon  change  of  variability  of  gains.  The  calculations  contained  in 
Table  18  afford  a  more  or  less  satisfactory  explanation  of  these 
exceptional  changes  in  the  coefficient  of  variation. 

For  the  purpose  of  measuring  most  effectively  the  changes  in- 
stituted in  the  rations,  the  quantities  of  the  different  feeds  con- 
sumed per  w'eek  have  been  converted  into  Scandinavian  feed  units. 
One  feed  unit,  according  to  this  system,  is  equal  to  i  lb.  of  standard 
grain,  such  as  corn,  or  its  equivalent  in  feeding  value.  According 
to  this  system,  in  the  case  of  pigs,  i  lb.  of  corn  is  equivalent  to  1.2 
lbs.  of  shorts  or  middlings,  and  to  6.0  lbs.  of  skim  milk.  On 
reference  to  Table  9^  of  the  Appendix  it  will  be  seen  that  in  Lot  II 
the  coefficient  of  variation  decreases  for  5  wrecks  and  then  abruptly 
increases  during  the  6th  week.  In  Lot  I,  the  decrease  continues 
for  4  weeks,  but  an  increase  occurs  during  the  5th  as  well  as  the 
6th  week.  Referring  now  to  Table  18,  it  will  be  seen  that  the 
number  of  feed  units  per  100  lbs.  live  weight  remains  at  a  com- 
paratively high  level  in  both  lots  for  the  first  5  weeks,  and  then 

"See  pages  574  to  577. 
"See  page  577. 


520 


Bl'Lletin   No.  165 


[July, 


Table  18. — Relation  of  Feed  to  Body  Weight  ix  Experiment  32 


Lot  I 

Lot  11 

Total 

Total 

Feed 

Total 

Total 

Feed 

feed 

weight 

units  per 

feed 

weight 

units  per 

units 

of 

100  lbs. 

units 

of 

100  lbs. 

per 

lot,* 

live 

per 

lot,» 

•  live 

lot 

lbs. 

weight 

lot 

lbs. 

weight 

1st  week    

257 

815 

31.5 

263 

822 

32.2 

2d    week    

265 

891 

29.7 

273 

883 

30.9 

3d    week    

314 

977 

32.1 

330 

964 

34.2 

4th  week   

318 

1072 

29.7 

323 

1069 

30.2 

5th  week   

359 

1172 

30.6 

373 

1177 

31.7 

6th  week   

326 

1308 

24.9 

370 

1318 

28.1 

7th  week   

339 

1369 

24.8 

394 

1396 

28.2 

8th  week   

369 

1494 

24.7 

416 

1528 

27.2 

9tli  week   

397 

1552 

25.6 

448 

1623 

27.6 

10th  week   

437 

1673 

26.1 

470 

1743 

27.0 

11th  week   

455 

1798 

25 . 3 

500 

1862 

26.9 

12th  week    

474 

1903 

24.9 

525 

2011 

26.1 

'That  is,  the  total  weight  of  the  lot  at  the  beginning  of  the  week. 


assumes  a  lower  level  rather  suddenly  during  the  6th  week.  Fur- 
thermore, in  Lot  I  this  lower  level  is  maintained  till  the  end  of 
the  experiment,  while  in  Lot  II  further  decreases  occur.  Turn- 
ing again  to  Table  9  of  the  Appendix,  it  will  be  seen  that  in  Lot  I, 
from  the  6th  week  to  the  end  of  the  experiment,  the  coefficient  of 
variation  maintains  practically  the  same  level,  while  in  Lot  II,  a 
notable  increase  occurs  at  the  beginning  of  the  8th  week,  coinci- 
dent with  a  decrease  of  one  unit  in  the  number  of  feed  units  per 
100  lbs.  live  weight,  establishing  a  higher  percentage  variability  for 
the  rest  of  the  experiment. 

Whether  this  correlation  is  really  significant  or  is  simply  a  more 
or  less  remarkable  coincidence,  we  are  not  prepared  to  say  definitely. 
It  is  at  least  highly  suggestive.  If  significant,  it  would  indicate 
that  the  effect  of  change  of  ration  on  change  of  variability  of  gains 
is  modified  by  the  relation  between  ration  and  body  weight  or  ra- 
tion and  nutritive  recjuirements. 

JVisconsin  Experiment  li'iih  Lambs. — An  experiment  performed 
at  the  \\'isconsin  Station  by  \V.  L.  Carlyle  is  of  considerable  in- 
terest in  this  connection.  Two  lots  of  lambs,  17  in  a  lot,  were  fed 
for  10  weeks  before  and  10  weeks  after  weaning.  The  lambs  in 
Lot  I  were  fed  coarsely  ground  corn,  while  those  in  Lot  II  re- 
ceived coarsely  ground  peas.  Before  w'eaning,  the  lambs  in  both 
lots  had  all  the  grain  they  would  eat.  After  weaning,  they  were 
limited  to  about  J4  lb.  per  capita  per  day.  The  statistical  data  con- 
cerning the  total  gains  in  weight  every  two  weeks  thruout  the  ex- 
periment, and  the  total  quantities  of  grain  consumed  per  lot  per 
period  of  two  weeks,  are  given  in  Table  19. 


Jpi3] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


521 


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522  Bulletin  No.  165  [July, 

Before  weaning,  the  variability  of  gains  decreased  continuously 
in  Lot  II,  while  in  Lot  I,  after  an  initial  marked  decrease,  it  re- 
mained practically  constant.  The  explanation  of  this  difference  in 
behavior  is  not  obvious  from  the  data  at  hand.  Possibly  the  marked 
increase  in  the  consumption  of  corn  by  Lot  I  from  the  first  to  the 
second  period  reduced  the  variability  of  the  gains  to  its  charac- 
teristic minimum,  which  subsequent  feeding  could  not  reduce ;  or 
possibly  the  explanation  of  the  difference  is  to  be  found  in  the 
different  Cjuantities  of  milk  obtained  from  the  dams  in  the  two  lots. 

At  the  time  of  weaning,  however,  the  change  in  variability 
of  the  two  lots  is  perfectly  intelligible  according  to  the  theory 
under  investigation,  i.e.,  that  an  increasing  feed  consumption 
(within  certain  limits  at  least)  tends  to  produce  more  uniform 
gains,  while  a  constant  or  decreasing  feed  consumption  tends  to 
produce  less  uniform  gains.  By  reference  to  the  table,  it  is  evident 
that  in  the  case  of  Lot  I  at  weaning  the  grain  ration  was  unaltered. 
The  withdrawal  of  milk  from  the  ration  therefore  occasioned  an 
increase  in  the  coefficient  of  variation.  In  the  case  of  Lot  II,  the 
withdrawal  of  milk  w^as  accompanied  by  a  compensating  increase 
in  the  consumption  of  grain,  and  the  coefficient  of  variation  re- 
mained practically  unaltered, 

Pennsylvania  Bxperiments  with  Steers. — We  shall  next  con- 
sider two  experiments  on  steers  performed  at  the  Pennsylvania 
vStation  by  Mairs  and  Risser,  a  statistical  resume  of  which  is  given 
in  Table  20. 

In  the  first  of  these  two  experiments,  the  mixed  meal  in  the 
ration  was  increased  for  the  first  6  or  8  weeks,  the  clover  hay  varied 
only  within  narrow  limits,  while  the  corn  stover  was  decreased. 
The  variability  of  the  gains  in  each  of  the  two  lots  decreased  for 
the  first  two  or  three  periods,  and  then  remained  practically  con- 
stant. In  the  second  experiment,  the  mixed  meal  was  increased 
continuously  from  the  first  of  the  experiment  to  the  sixth  or  sev- 
enth period,  after  which  a  slight  decrease  occurred.  The  corn 
stover  in  Lot  I  was  consumed  in  rather  constant  quantities,  until 
the  last  period,  when  a  decrease  occurred.  In  Lot  II,  a  more  or 
less  regular  decrease  occurred  from  start  to  finish.  The  quantity 
of  clover  hay  consumed  in  both  lots  was  fairly  constant.  It  will  be 
seen  that  the  rations  of  this  experiment,  especially  that  of  Lot  I, 
increased  in  general  as  the  experiment  progressed.  Consequently, 
the  variability  of  gains  in  both  lots  decreased  progressively  from 
start  to  finish,  the  decrease  being  more  noticeable  in  Lot  I. 

U'obiirn  Experiments  ivitli  Sheep. — The  last  experiment  that 
we  shall  consider  is  one  performed  by  Voelcker  at  the  Woburn 
Experimental  Farm  in  1895-6  on  sheep.  The  data  are  given  in 
Table  21. 

The  ration  in  general  was  increased  at  times  as  the  experiment 
progressed.     In  no  lot,  however,  is  there  a  very  decided  tendency 


■fp^i] 


Uncertainty  in  Intekpret.'iTion  of  Feeding  Experiments 


523 


Table  20. — Change  in  Variarilitv  of  Total  Gains  in  Weight  of  Two  Lots 
OF  Steers,  and  Total  Feed  Consumption  per  Lot  per  Period 

(All  weights  expressed  in  pounds) 


Total  gain 


Statistical  data   of   total 
s;ains 


Mean 


Standard 
deviation 


Coeffi- 
cient of 
variation 


Total  feed  consumption  by 
2-\veek  periods 


Clover 
hay 


Corn 
stover 


Mixed 
meal 


Lot   I.      1 

2  Steers  (35) 

In     2  weeks. .  . 

16.6 

6.30 

38.02 

984 

74S 

1825 

In    4  weeks. .  . 

51.4 

9.67 

18.81 

1147 

812 

2467 

In    6  weeks . . . 

98.4 

14.90 

15.14 

971 

678 

2769 

In     8  weeks . .  . 

113.3 

17.71 

15.63 

1098 

767 

2909 

In  10  weeks . . . 

148.4 

25.01 

16.85 

1016 

589 

2950 

In  12  weeks. .  . 

166.8 

23.48 

14.08 

1025 

648 

3023 

In  14  weeks. . . 

201.5 

32.20 

15.98 

1023 

617 

3199 

In  16  weeks. .  . 

230 . 4 

41.90 

18.19 

10.50 

563 

2980 

In  18  weeks. .  . 

26<) .  ?. 

43. 4S 

16.15 

1050 

533 

2930 

Lot  II.     12  Steers  (35) 


In     2  weeks.  . . 

9.1 

15.13 

166.60 

1020 

848 

1921 

In     4  weeks . . . 

49.7 

11.20 

22.51 

1134 

953 

2464 

In    6  weeks. . . 

Sl.O 

15. 75 

19.44 

964 

786 

2941 

In     8  weeks. .  . 

111.7 

21.05 

18.84 

1079 

847 

3122 

In  10  weeks. .  . 

134.8 

21.78 

16.16 

1058 

672 

2968 

In  12  weeks. . . 

160.7 

29.03 

18.07 

1029 

651 

3088 

In  14  weeks. . . 

188.6 

31.00 

16.44 

1019 

619 

3134 

In  16  weeks. .  . 

210.0 

33.97 

16.18 

1041 

447 

2912 

In  18  weeks. .  . 

247.7 

3S .  1  s 

15.41 

993 

528 

2802 

Lot  I.     1 

2  Steers   (30) 

In     18  days. .  . 

13.2 

10.43 

78.72 

In     32  davs..  . 

55.1 

17.67 

32.08 

1084 

821 

2367 

In     46  days. . . 

84.6 

23.33 

27.58 

1042 

840 

2872 

In     60  days. . . 

115.9 

24.34 

21.00 

1134 

827 

3038 

In     74  days. .  . 

149.2 

30.25 

20.27 

988 

798 

3118 

In     88  days. .. 

184.4 

38 .  06 

20.64 

1030 

850 

3298 

In   102  davs..  . 

208 . 9 

37.17 

17.79 

1130 

804 

3339 

In    116  days. .  . 

22S .  7 

40 .  62 

1 7 .  76 

1105 

605 

3231 

Lot  II. 

12  Steers   ( 

36) 

In     18   days. . . 

34.  1 

19.17 

56.25 

In     32  days. .. 

73.0 

21.08 

28.88 

1043 

895 

2485 

In     46  days. .. 

95.4 

30.. 39 

31.85 

1091 

811 

2882 

In     60  days.. . 

128.2 

33.36 

26.02 

1079 

759 

3061 

In     74  days. .. 

1.56.4 

34.80 

22.25 

958 

659 

3093 

In     88   days... 

180.4 

41.18 

22.83 

1028 

795 

3232 

In   102   davs. . . 

203.4 

44.14 

21.70 

1137 

390 

3224 

In   116   days. . . 

226 . 9 

41.92 

18.48 

1053 

491 

3141 

for  the  gains  to  become  more  uniform  after  the  first  63  days;  in 
one  lot  (III)  the  coefficient  of  variation  at  the  end  of  63  days  is 
practically  the  same  as  that  at  the  end  of  87  days,  while  in  one 
lot  (I)  it  is  less.  The  explanation  of  this  state  of  affairs  we  be- 
lieve is  to  be  found  in  the  weather  conditions  at  the  time  of  the 
experiment,  which  are  described  by  Voelcker  as  follows : 

"The  winter  of  1895-6  will  lone:  he  remembered  as  one  of  an  altogether 
exceptional  character,  if  'winter'  indeed  it  could  be  called.  Thougli  there  was 
an  almost  entire  absence  of  frost,  yet  from  the  commencement  until  the  middle 


524 


Bulletin  No.  165 


[July, 


Table  21. — Change  in  Variability  of  Total  Gains  in  Weight  of  Four  Lots 

OF  Sheep  (22) 

(All  weights  expressed  in  pounds) 


Statistical  data  of  total  gains  in  weight 

Total  gains 

Mean 

Standard 
deviation 

Coeffi- 
cient of 
variation 

Mean 

Standard 

deviation 

1 

<    Coeffi- 
cient of 
variation 

Lot  I.     15  Sheep 

Lot  III.     14  Sheep 

In  34  days.  . . . 

In  63  days 

In  87   days 

15.27 
25.87 
31.53 

6.248 

7.957 

10.020 

40.92 

30.76 

•     31.78 

15.07 
24.36 
27.36 

8.311 
8.217 
9.216 

55.15 
33.73 
33.68 

Lot  II.     15  Sheep 

Lot  IV.     13  Sheep 

In   34   days 

In  63  days 

In  87  days 

15.07 
25 .  20 
20 .  07 

4.074 
6.524 
6.424 

27.03 
25.89 
22.10 

18.46 
28.31 
30.07 

7.812 
9.738 
8.922 

42.32 
34.40 
29 .  67 

of  January  cold  winds  were  very  prevalent,  together  with  a  continual  dampness 
and  general  'mugginess'  of  atmosphere,  this  weather  proving  very  trying  for 
sheep,  and  in  the  neighborhood  of  the  Woburn  farm  flockmasters  lost  several 
of  their  sheep.  *  *  *  Nor  did  our  experiments  fare  any  better,  for  in  all 
we  lost  six  sheep." 

That  the  weather  conditions  were  unfavorable  to  fattening  is 
suggested  by  the  average  daily  gains  per  sheep  for  the  three  periods 
of  the  experiment.  The  first  period  was  34  days  in  length,  the 
second,  29,  and  the  third,  24.  For  Lot  I,  these  three  averages  are, 
respectively,  0.449,  0-3<j6,  and  0.236  lb. ;  Lot  PI,  0.443,  0.349,  and 
0.161  lb. ;  and  Lot  III,  0.543,  0.340,  and  0.074  lb. 

Conclusions. — In  the  above  presentation  of  experimental  data 
concerning  the  change  in  variability  of  gains  in  weight  within  the 
lot  as  the  period  of  observation  increases,  no  attempt  to  select  ex- 
periments favorable  to  any  particular  theory,  or  to  discard  any 
experiments  except  those  whose  data  were  too  incomplete  for  ad- 
vantageous study,  has  been  made.  The  data  given  in  Tables  8  to 
21  inclusive  represent  practically  all  the  data  of  this  nature  that 
we  have  thus  far  collected.  There  is  every  reason  for  believing, 
therefore,  that  the  conclusions  to  which  they  lead  are  unbiased  and 
have  a  general  application. 

It  is  evident,  however,  that  no  single  explanation  can  apply  to 
the  change  in  variability  in  all  the  experiments  reviewed.  The 
factors  involved  are  evidently  numerous,  and  in  many  cases  even 
the  chief  factors  cannot  be  detected,  either  because  the  experimental 
conditions  were  not  described  in  sufficient  detail,  or  because  the  lots 
were  so  small  that  the  casual  fluctuations  in  any  statistical  constant, 
such  as  a  coefficient  of  variation,  incident  to  all  feeding  trials,  ob- 
scured progressive  changes. 

We  believe,  however,  that  a  general  statement  may  be  made  that 
will  sum  up  in  a  satisfactory  manner  the  chief  indications  of  the 
several  experiments  just  studied.    //  seems  probable  that  conditions 


ip/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  S2S 

favorable  to  grozvth  or  fattening  in  general  are  favorable  to  uni- 
form rates  of  grozcth  or  fattening  ivithin  a  group  of  animals. 

As  a  first  corollary  to  this  rule:  Given  tzvo  groups  of  animals 
under  difJerent  conditions,  that  group  grozving  or  fattening  at  the 
more  rapid  rate  zvill,  in  general,  tend  to  exhibit  the  more  uniform 
gains,  uniformity  being  measured  on  the  percentage  scale. 

Considering  next  groups  of  animals  under  changing  conditions, 
it  follows  that  if  change  in  ration,  zveather,  or  other  conditions  is 
resulting  continually  in  conditions  more  faz'orable  to  grozvth  or  fat- 
tening, the  gains  zdthin  the  group  zvill  tend  to  become  more  and 
more  uniform.  The  full  significance  of  this  corollary  is  not  at 
once  evident.  Consider  the  ration  of  experimental  animals,  for  in- 
stance. The  feed  requirement  of  animals  per  individual  increases 
during  the  course  of  a  feeding  experiment  with  increasing  age  and 
body  weight.  Therefore,  a  constant  ration  thruout  an  experiment 
results,  not  in  equally  favorable  conditions  for  growth  or  fat- 
tening for  successive  periods,  but  in  progressively  less  favorable 
conditions,  tho  the  rate  of  this  change  may  be  gradual.  Hence  we 
have  found  in  the  above  study  that  a  constant  ration  is  often  ac- 
companied by  a  decreasing  uniformity  of  gains,  tho  the  decrease 
may  be  slight  and  may  be  deferred.  Often  a  constant  ration  is 
accompanied  by  no  progressive  change  in  the  uniformity  of  gains, 
especially  if  the  period  during  which  the  ration  remains  constant  is 
short,  the  change  from  favorable  to  less  favorable  conditions  being 
too  slight  to  produce  any  noticeable  effect  upon  the  coefficient  of 
variation.  One  would  expect  the  latter  state  of  affairs  to  occur  with 
mature  rather  than  with  immature  animals.  Similarly,  an  increas- 
ing ration  does  not  necessarily  mean  continually  more  favorable 
conditions,  unless  the  increase  keeps  pace  with  the  increasing  re- 
quirements. 

The  above  conclusions  are  merely  tentative  and  may  be  modi- 
fied by  further  investigation.  In  fact,  the  experimental  data  we 
have  considered  indicate  certain  minor  exceptions.  In  the  first 
place,  it  seems  that  no  matter  what  the  ration  be  or  what  changes 
in  the  ration  be  instituted,  the  gains  at  the  very  beginning  of  an 
experiment  are  generally  extremely  variable,  and  the  extreme  vari- 
ability undergoes  a  considerable  decrease  in  a  very  short  time. 
This  may  be  the  result  of  a  general  change  in  ration  made  a 
short  time  before  the  experiment  started  and  of  a  comparatively 
rapid  adaptation  of  the  animals  to  this  change.  Again,  for  any 
given  group  of  animals  and  any  given  set  of  experimental  condi- 
tions, there  seems  to  be  a  minimum  variability  characteristic  of  the 
particular  experimental  conditions  and  the  particular  animals  se- 
lected for  experimental  purposes,  beyond  which  it  is  impossible  to 
go  no  matter  how  increasingly  favorable  the  feeding  or  other  con- 


526  Bulletin  No.  165  [July, 

ditions  may  be  made.  Further,  a  general  impression  we  have  re- 
ceived from  the  above  study  is  that  the  rate  of  decrease  of  the 
coefficient  of  variabiHty  under  favorable  fattening  conditions  be- 
comes gradually  less  as  this  minimum  is  approached. 

It  appears  that  the  effect  of  changes  in  experimental  conditions 
on  the  variability  of  gains  is  more  pronounced  and  more  noticeable 
in  the  case  of  sheep  than  in  the  case  of  either  steers  or  swine.  This 
would  indicate  that  sheep  are  more  susceptible  to  such  changes  than 
other  farm  animals,  a  conclusion  that  probably  embodies  the  con- 
sensus of  opinion  of  investigators  of  the  feed  requirements  and  ca- 
pacities of  farm  animals. 

(e)  Physiological  Selection  of  Animals  For  Feeding  Bxperiments 

In  considering  other  methods  of  conducting  feeding  experiments 
than  those  above  discussed,  the  object  of  which  is  to  secure  more 
uniform  behavior  of  the  individual  experimental  animals,  or,  in 
other  words,  to  reduce  the  experimental  error,  we  shall  investigate 
a  plan  the  essence  of  which  is  the  selection  for  experiment  of  only 
those  animals  that  in  the  course  of  a  preliminary  feeding  period 
have  proved  to  be  functionally  similar.  This  plan  is  apparently  in 
vogue  at  several  stations  in  one  modified  form  or  another.  The 
most  forceful  arguments  in  its' favor  are  its  simplicity  and  a  feeling 
that  is  difficult  to  evade  that  it  is  necessarily  very  effective  in  re- 
ducing to  a  minimum  the  effect  of  individuality. 

It  is  desired,  for  instance,  to  undertake  an  experiment  wnth  the 
purpose  of  comparing  the  fattening  value  of  two  rations.  For 
practical  reasons,  we  will  say,  it  has  been  decided  to  use  two  lots 
of  ten  animals  each.  From  the  station  herd,  thirty  animals, 
say,  of  uniform  age,  breed,  sex,  and  general  appearance  are 
selected.  These  thirty  animals  are  put  on  a  uniform  ration  for  a 
period  of  two  to  four  wrecks,  or  thereabouts.  At  the  end  of  this 
preliminary  period,  the  individual  gains  made  by  the  animals  are 
consulted,  and  those  twenty  animals  are  picked  for  the  experiment 
whose  gains  cluster  closest  about  the  average  gain  for  the  lot. 
During  this  preliminary  period,  these  twenty  animals  have  behaved 
very  similarly  so  far  as  the  rate  of  fattening  is  concerned,  and  it 
is  assumed  that  they  will  continue  on  similar  behavior  during  the 
experiment  proper.  This  procedure  may  be  modified  as  follows : 
Instead  of  putting  the  original  thirty  animals  on  a  uniform  ration, 
they  may  be  divided  into  two  lots  of  fifteen  each,  and  these  two  lots 
may  be  put  on  the  two  rations  that  are  to  be  investigated.  After 
several  weeks  the  ten  animals  of  each  lot  that  have  made  the  most 
representative  gains  are  selected  and  the  experiment  is  continued 
on  these  animals  only.     This  latter  procedure  has  the  advantage 


i 


^913]  Uncertainty  in  Interpretation  of  Feeding  Experiments  527 

over  the  former  in  that  it  need  not  be  assumed  that  because  ani- 
mals gain  at  a  similar  rate  on  one  ration,  they  will  do  so  on  another. 
\\'e  are  assuming  merely  that  they  will  continue  to  gain  uniformly 
on  the  same  ration. 

By  this  selection  of  animals,  which  we  will  call  a  physiological 
selection,  we  are  presumably  excluding  abnormal  individuals  from 
the  experiment  as  well  as  securing  a  lot  of  animals  in  which  in- 
dividuality is  reduced  to  within  satisfactory  limits. 

Theoretical  Considerations. — We  feel  that  there  are  certain 
theoretical  objections  to  such  a  physiological  selection  of  experi- 
mental animals.  .Assuming  that  the  selection  is  effective  in  lower- 
ing variability,  it  seems  far  from  improbable  that  the  arbitrary 
selection  of  animals  made  after  the  preliminary  test^  will  detract 
from  the  value  of  the  subsequent  experiment  to  the  practical  farmer, 
since  the  animals  actually  experimented  upon  cannot  be  regarded 
as  a  random  sample  nor  even  as  a  sample  that  the  farmer  could 
approximately  duplicate.  The  experimental  animals  have  been 
drawn  from  a  class  that  cannot  be  defined.  Suppose  in  the  prelimi- 
nary test  we  decide  to  exclude  from  further  experiment  all  ani- 
mals that  have  not  made  an  average  daily  gain  of  at  least  a  certain 
magnitude,  which  we  shall  arbitrarily  agree  upon,  and  all  animals 
that  have  made  greater  average  daily  gains  than  another  arbitrary 
magnitude.  Does  this  constitute  a  practicable  definition  of  the  class 
of  animals  from  which  we  have  selected  the  animals  for  our  ex- 
periment ?  Can  we  say  that  the  conclusions  ultimately  drawn  from 
the  experiment  apply  to  animals  of  a  certain  species  gaining  be- 
tween a  and  h  pounds  per  day  under  such  and  such  conditions? 
We  hardly  think  so.  If  there  is  anything  that  the  collection  of 
individual  data  from  time  to  time  during  a  feeding  trial  shows,  it 
is  this, — that  under  the  same  experimental  conditions  the  same 
animals  will  unaccountably  change  in  weight  in  a  very  irregular 
manner,  now  losing  in  weight  or  showing  very  poor  gains  for  days 
at  a  time  and  subsequently  exhibiting  phenomenal  gains,  so  that 
animals  cannot  be  classified  even  approximately  by  the  gaining 
qualities  exhibited  during  a  brief  preliminarx'  test.  The  exclusion 
of  "abnormal"  individuals,  i.e.,  individuals  in  a  pathological  condi- 
tion due  to  constitutional  defects,  disease,  etc.,  from  a  feeding  ex- 
periment is-  perfectly  legitimate,  but  we  doubt  whether  anyone  is 
competent  to  pick  out  "abnormal"  individuals  after  such  a  test  on 
the  basis  of  gains  in  weight.  Certainly  exceptional  functional  char- 
acteristics are  no  sure  indices  to  abnormal  functional  characteris- 
tics, and  the  exclusion  of  individuals  exhibiting  rather  exceptional 

*The  objection  of  course,  is  not  directed  at  the  preliminary  period  as  such, 
but  at  the  practice  of  utilizing  this  period  for  the  physiological  selection  of  ani- 
mals. As  has  been  shown  above,  the  preliminary  feeding  period  is  a  very  nec- 
essary accessory  to  the  experiment  proper. 


528  Bulletin  No.  165  [July, 

functioning  for  the  purpose  of  securing  an  artificially  homogeneous 
lot  will  result  in  an  unfair  test  of  the  problem  which  it  is  desired 
to  solve. 

Does  Physiological  Selection  BHininate  Poor  Gainer's f — The 
objections  to  such  a  physiological  selection  of  animals  for  feeding 
experiments  as  that  described  above  are  not  all  theoretical.  It  may 
be  attacked  on  the  ground  of  its  efficacy  in  accomplishing  the  pur-, 
poses  which  it  is  supposed  to  serve.  In  testing  such  efficacy  we 
know  of  no  more  suitable  data  than  those  collected  by  J.  B.  Lawes 
at  the  Rothamsted  Station.  The  six  lots  of  sheep  that  Lawes  ex- 
perimented with  contained  40  to  46  animals  each.  The  individual 
gains  for  every  four  weeks  of  the  experiment  were  carefully  de- 
termined and  reported.  Suppose  we  consider  the  first  four  weeks 
of  each  experiment  as  a  preliminary  test  for  the  purpose  of  af- 
fording a  basis  for  a  physiological  selection  of  the  animals.  On 
the  basis  of  the  gains  obtained  during  this  first  four-week  period, 
we  shall  divide  each  of  the  six  lots  of  sheep  into  sub-lots,  or  groups, 
of  10  sheep  each,  the  first  group  in  each  lot  to  include  the  10  sheep 
making  the  ten  best  gains  in  the  lot,  the  second  group  to  include 
the  10  sheep  making  the  ten  next  best  gains,  and  so  on  for  the 
third,  fourth,  and,  in  the  case  of  the  Cotswold  sheep,  the  fifth 
groups.  We  now  wish  to  know  what  gains  these  groups  make 
during  the  remainder  of  the  experiment. 

It  is  evident  from  the  results  shown  in  Table  22  that  any  selec- 
tion of  animals  made  according  to  the  preliminary  gains  is  prac- 
tically without  effect  on  the  gains  obtained  in  a  subsequent  feeding 
period  of  16  weeks.  In  every  lot,  the  average  preliminary  gains 
of  the  different  groups  are  quite  distinctly  separated  from  each 
other,  the  average  gain  of  the  last  group  constituting  only  30  to 
50  percent  of  the  average  gain  of  the  first  group.  However,  in 
every  case,  at  the  end  of  the  subsequent  feeding  periods  there  is 
little  to  choose  as  regards  average  gain  in  weight  between  the 
different  groups.  In  only  two  out  of  the  six  lots  is  the  greatest 
average  gain  during  the  subsequent  feeding  period  made  by  the 
first  group,  while  in  one  lo't,  the  crossbred  ewes,  the  last  group 
exhibits  the  highest  average  gain.  In  two  lots,  Group  II  makes 
the  best  average  gain,  and  in  one  lot.  Group  III  has  this  distinction. 

Does  Physiological  Selection  Reduce  the  Experimental  Error? 
— Let  us  next  consider  the  effectiveness  of  physiological  selection 
in  reducing  individuality  in  a  subsequent  feeding  period,  as  re- 
gards gains  in  weight.  In  a  study  of  this  phase  of  the  question, 
we  have  adopted  the  following  procedure.  We  still  regard  the  first 
four  weeks  of  Lawes'  experiments  as  a  preliminary  period,  the 
gains  in  weight  during  this  period  affording  the  basis  for  physio- 
logical  selection.     We  find  the  average  gain  of  each  lot  during 


« 


■rp^j] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


529 


Table  22. — Effect  of  Physiological  selection  on  average  Gains 
(All  weights  expressed  in  pounds) 


Average  weights  and 
gains  per  group 


Group 
I 


Group 
II 


Group 
III 


Group 
IV 


Group 


40   Hampshire  Wethers    (2T 


Initial  weight  . . . 
Preliminary  gain 
Gain  in  4  weeks. 
Gain  in  8  weeks. 
Gain  in  12  weeks. 
Gain  in  16  weeks. 
Gain  in  20  weeks. 
Gain  in  22  weeks. 


11G.8 
16.0 
9.4 
20.0 
31.5 
43.2 
54.1 
60.2 


113.1 
11.6 
7.6 
16.4 
26.8 
36.8 
50.9 
59.5 


115.4 
9.3 
11.1 
21.1 
33.3 
46.0 
55.2 
63.5 


10S.5 
5.7 
9.0 
17.0 
27.0 
38.0 
48.5 
54.8 


40   Sussex  Wethers    (27) 


Initial  weight  .  . .  . 
Preliminary  gain  . 
Gain  in  4  w^eeks. 
Gain  in  8  weeks. 
Gain  in  12  weeks. 
Gain  in  16  weeks. 
Gain  in  20  weeks. 
Gain  in  22  weeks. 


92.3 
14.1 
7.5 
13.2 
21.5 
27.0 
37.6 
44.9 


86.9 
11.1 
6.5 
12.4 
20.8 
25.4 
37.7 
44.4 


S6.3 
9.3 
7.0 
11.6 
19.0 
22.7 
34.2 
.39.9 


86.5 
5.8 
6.0 
11.0 
19.7 
25.1 
36.7 
42.6 


40  Leicester  Wethers   (29) 


Initial  weight  .  . .  . 
Preliminary  gain 
Gain  in  4  weeks. 
Gain  in  8  weeks. 
Gain  in  12  weeks. 
Gain  in  16  weeks. 


100.2 
10.9 
5.1 
16.5 
27.3 
36.6 


104, 

8. 

4, 

17, 

29 


41.0 


102.4 
7.1 
1.6 

14.5 
26.4 
36.4 


98.4 
3.5 
3.3 
15.0 
25.1 
34.2 


46  Cotswold  Wethers 

(28) 

Initial  weight   

116.4 

116.6 

121.0 

123.9 

121.2 

Preliminary   gain    

17.9 

15.9 

14.6 

12.9 

8.7 

Gain  in     4  weeks 

14.3 

13.2 

13.4 

10.1 

12.3 

Gain  in     8  weeks 

29.0 

26.2 

26.5 

24.1 

23.8 

Gain  in  12  weeks 

39.3 

36.1 

38.4 

35.4 

32.2 

Gain  in  16  weeks 

52 . 3 

47.4 

51.8 

49.4 

44.1 

40  Crossbred  Wethers  (29) 


Initial  weight  .  . . 
Preliminary  gain  . 
Gain  in  4  weeks. 
Gain  in  8  weeks. 
Gain  in  12  weeks. 
Gain  in  16  weeks. 


95.5 
12.1 
6.3 
15.9 
29.3 
3,-).  9 


95.8 
9.5 
6.9 
16.9 
28.9 
36.1 


94.9 
8.2 
7.5 

16.8 
28.1 
35.6 


94.2 
5.2 
6.9 
16.3 
27.5 
35.4 


40  Crossb 

red  Ewes 

(29) 

Initial  weights 

91.6 

88.7 

91.2 

93.5 

Preliminary   gain    

10.9 

8.7 

6.9 

3.4 

Gain  in     4  weeks 

5.2 

5.9 

4.5 

7.4 

Gain  in     8  weeks 

16.2 

16.6 

14.5 

19.2 

Gain  in  12  weeks 

26.2 

27.0 

24.1 

29.2 

Gain  in  16  weeks 

35.3 

34.8 

33.0 

36.9 

530  Bulletin  No.  165  [July, 

this  preliminary  period,  and  select  from  each  lot  only  those  ani- 
mals whose  preliminary  gains  lie  approximately  within  i  lb.  of 
the  average  gain  for  the  lot.  Thus,  the  40  Hampshire  wethers 
gained  on  an  average  10.72  lbs,  during  the  preliminary  period,  and 
we  have  therefore  selected  those  wethers  in  the  lot  gaining  10,  11, 
or  12  lbs.  during  this  period.  The  40  Sussex  wethers  gained  10.07 
lbs.  during  the  first  period,  and  therefore  in  this  group  only  wethers 
gaining  9,  10,  or  1 1  lbs.  in  the  first  four  weeks  have  been  selected. 
A  similar  selection  has  been,  made  in  the  other  four  lots.  The  vari- 
ability of  the  total  gains  made  in  these  selected  lots  was  then  deter- 
mined for  this  preliminary  period,  the  subsequent  four  weeks,  eight 
weeks,  etc.  A  comparison  of  these  coefficients  with  the  correspond- 
ing coefficients  for  the  complete  lots  indicates  the  effect  of  our 
selection.    The  data  for  this  study  are  contained  in  Table  23. 

In  the  case  of  the  Hampshire  wethers,  during  the  preliminary 
four  weeks  the  entire  lot  made  gains  possessing  a  coefficient  of 
variation  of  37.14.  Fourteen  of  the  40  wethers  have  been  selected, 
the  selected  wethers  including  all  that  gained  either  10,  11,  or  12 
lbs.  during  this  preliminary  period.  The  coefficient  of  variation  for 
this  selected  lot  for  the  preliminary  period  is  7.68,  a  very  low  value, 
resulting  from  the  artificial  selection.  During  the  subsequent  four 
weeks  the  gains  of  the  selected  wethers  exhibit  a  coefficient  of 
variation  of  21.33,  the  corresponding  coefficient  for  the  entire  lot 
being  only  30.54.  This  difference  between  the  coefficients  of  varia- 
tion of  the  complete  lot  and  the  selected  lot  decreases  as  the  ex- 
periment progresses  until  at  the  end  of  22  weeks,  the  two  are,  to 
all  intents  and  purposes,  equal.  In  the  case  of  this  lot,  a  very  rig- 
orous physiological  selection  of  animals  has  resulted  in  a  sub-lot 
which,  at  the  end  of  a  subsequent  22-week  feeding  period,  .is  prac- 
tically nothing  better  than  a  random  sample  of  the  complete  lot. 

In  the  case  of  the  40  Sussex  wethers,  the  46  Cotswold  wethers, 
and  the  40  Leicester  wethers,  a  similar  physiological  selection  re- 
sults at  the  end  of  the  subsequent  feeding  period  in  a  selected  lot 
whose  coefficient  of  variation  is  4  to  5  percent  lower  than  that  of 
the  corresponding  complete  lot.  In  the  case  of  the  40  crossbred 
wethers,  a  precisely  similar  selection  results  in  a  lot  which  at  the 
end  of  the  subsequent  feeding  period,  is  not  to  be  differentiated 
from  the  complete  lot  as  regards  variability  of  gains.  In  the  case 
of  the  40  crossbred  ewes,  the  same  method  of  physiological  selec- 
tion results  in  a  more  variable  lot  thruout  the  suljsequent  feeding 
period. 

These  results  indicate  that  a  rigorous  physiological  selection  of 
animals — much  more  rigorous  than  would  be  practicable  in  the 
ordinary  feeding  experiment — sometimes  fails  utterly  to  secure 
greater  uniformity  of  gains  after  a   subsequent   feeding  period. 


^9^3]                 U-N'CERTAIXTV    IX    ] 

xterpretation  of  Feeding  Experiments 

531 

Table  23.— Effect 

OF  Physiological  Selection  on  the  Variability  or 
(All  gains  e.xpressed  in  pounds) 

Gains 

Data   concerning   gains   of 
complete  lot 

Data   concerning   gains   of 
selected  lot 

Mean 

Standard 
deviation 

Coeffi- 
cient of 
variation 

Mean 

Standard 
deviation 

1     Coeffi- 
cient of 
variation 

40   Hampshire  Wethers   (14  Selected) 

Preliminary   gains. .  . 

10.72 

3.981 

37.14 

11.21 

.861 

7.68 

Gains  in     4  weeks. .  . 

9.62 

2.938 

30.54 

9.64 

2.0.56 

21.33 

Gains  in    8  weeks. . . 

19.17 

4.868 

25.. 39 

18.79 

4.280 

22.79 

Gains  in  12  weeks.. . 

30.30 

7.366 

24.31 

29.93 

5.824 

19.46 

Gains  in  16  weeks.. . 

41.87 

9.827 

23.47 

41.11 

8.918 

21.69 

Gains  in  20  weeks. . . 

52.07 

9 .  533 

18.31 

51.82 

8.930 

17.23 

Gains  in  22  weeks. .  . 

59 .  H9 

9.612 

16.  IS 

59 .  6S 

9.25S 

15.51 

40  Sussex  Wethers   (14  Selected) 

Preliminary   gains. .  . 

10.07 

3.364 

33 .  39 

10.29 

.  587 

5.70 

Gains  in    4  weeks. .  . 

6.75 

2.557 

37.86 

7.29 

2.118 

29.05 

Gains  in    8  weeks. . . 

12.05 

3.074 

25.51 

12.36 

2.408 

19.48 

Gains  in  12  weeks. .. 

20.25 

3.910 

19.31 

20.71 

3.452 

16.67 

Gams  in  16  weeks. .. 

25.07 

4.534 

18.09 

24.80 

3.668 

14.80 

Gains  in  20  weeks.. . 

36.22 

5.125 

14.15 

37.63 

3.882 

10.32 

Gains  in  22  weeks... 

42.65 

5.700 

13.36 

44.02 

3.634 

8.26 

46  Cotswold  Wethers  (18  Selected) 

Preliminary    gains. .  . 

14.46 

3.338 

23.09 

14.22 

.712 

5.01 

Gains  in    4  weeks. .  . 

12.70 

4.101 

32.30 

11.89 

4.713 

39.64 

Gains  in    8  weeks. . . 

26.11 

5.346 

20.48 

25.28 

5.031 

19.90 

Gains  in  12  weeks. . . 

36.64 

6.967 

19.01 

36.99 

6.591 

17.82 

Gains  in  16  weeks.  . . 

40.42 

S.731 

17.67 

50.82 

6.933 

13.64 

40  Leicester  Wethers  (15  Selected) 

Preliminary   gains. .  . 
Gains  in    4  weeks. .  . 

7.50 
3.50 

3.017 
4.117 

40.23 

7.40 
1.60 

.611 
3.592 

8.26 

Gains  in     8  weeks. . . 

15.92 

5.392 

33.87 

15.60 

4.348 

27.87 

Gains  in  12  weeks. . . 

27.17 

7.035 

25 .  89 

27.80 

6.134 

22.06 

Gains  in  16  weeks. .  . 

37.07 

8.229 

22.20 

37.98            6.847 

18.03 

40  Crossbred  Wethers    (IS   Selected) 

Preliminary   gains. .  . 

8.75 

2.653 

30.32 

9.11 

.657 

7.21 

Gains  in    4  weeks. .  . 

6.90 

2.567 

37.20 

7.50 

1 .  572 

20.96 

Gains  in    8  weeks. . . 

16.47 

3.529 

21.43 

17.11 

3.089 

18.05 

Gains  in  12  weeks. . . 

28.45 

4.477 

15.73 

28.67 

4.819 

16.81 

Gains  in  16  weeks. . . 

35.75 

5.422 

15.16 

35.93 

5.370 

14.95 

40   Crossbred   Ewes    (15   Selected) 

Preliminary    gains... 

7.47 

2.976 

39.84 

7.13 

.806 

11.30 

Gains  in    4  weeks. .  . 

5.75 

2.817 

49.00 

4.80 

2.663 

55.48 

Gains  in     8  weeks. . . 

16.62 

3.953 

23.78 

15.27 

3.785 

24.80 

Gains  in  12  weeks. . . 

26.62 

4.316 

16.21 

25.27 

4.139 

16.38 

Gains  in  16  weeks. .  . 

35.03 

5 .  170 

14.76 

33 .  67 

5.965 

17.72 

sometimes  has  r 

lo  marked  effect  on  the  subsequent  variabilit} 

%  and 

sometimes  does 

succeed  in  its  purpose  to  a  greater  or  less  e 

xtent. 

From  the  data 

ust  analyzed  one  would  infer  that  the  chanc 

es  are 

no  better  than  e 

ven  that  physiological  selection  as  rigorous  a 

s  that 

employed  will  a 

ccomplish 

1  its  purp 

ose  to  an 

y  sensible 

'  degree. 

S32  Bulletin  No.  165  [July, 

Suppose,  next,  we  test  the  effect  of  a  slightly  less  rigorous 
physiological  selection;  for  instance,  a  selection  that  would  be  much 
more  suitable  for  experiment  station  purposes.  We  will  take  the 
lot  of  40  Sussex  wethers,  because  in  this  lot  the  method  of  selec- 
tion already  tested  has  yielded  a  lot  more  uniform  as  compared 
with  the  corresponding  complete  lot  than  any  of  the  other  lots. 
At  the  end  of  a  subsequent  22-week  feeding  period,  the  coefficient 
of  variation  of  total  gains  for  the  complete  lot  is  found  to  be  13.36, 
and  for  the  selected  lot,  8.24,  or  over  5  percent  less.  In  our  sec- 
ond selection,  instead  of  taking  only  those  wethers  that  gained  9, 
10,  and  II  lbs.  during  the  preliminary  four  weeks,  i.e.,  14  wethers, 
we  will  take  all  wethers  that  gained  8,  9,  10,  11,  or  12  lbs,  during 
the  same  period.  This  gives  a  selected  lot  of  24  wethers  out  of 
the  forty.  The  statistical  data  as  regards  this  lot,  the  remaining 
16  wethers,  and  the  complete  lot  of  40  withers  are  given  in  Table 

24.  , 

The  results  of  this  selection  are  remarkable.  The  coefficient  of 
variation  of  the  24  selected  wethers  for  the  preliminary  period  is 
13.02,  and  that  for  the  16  remaining  wethers  that  were  not  selected, 
51.95.  For  the  next  4  weeks,  the  coefficient  for  the  selected  wethers 
is  38.14,  and  for  the  unselected,  36.20.  For  the  22  weeks  the 
two  coefficients  are,  in  order,  14.80  and  11.27.  The  failure  of 
this  method  of  physiological  selection  in  this  case  is  obvious. 

Conclusions. — The  results  given  in  Tables  22,  23,  and  24  can 
bear  but  one  interpretation.  The  gain  exhibited  by  an  animal  dur- 
ing a  given  period  of  time  affords  little  information  as  regards 
what  gains  it  will  make  in  subsequent  periods,  even  tho  the  experi- 
mental conditions  are  as  far  as  possible  unchanged ;  hence  the  fail- 
ure of  moderate  physiological  selection  and  the  uncertain  effect  and 
occasional  failure  of  even  the  most  rigorous  physiological  selection. 
Our  conclusion  is,  therefore,  that  physiological  selection  is  neither 
necessary  nor  desirable,  and  that  even  when  conducted  in  the  most 
rigorous  manner  its  effect  in  reducing  experimental  error  is  prob- 
lematical. It  must  be  noted  also  that  the  preliminary  period  upon 
which  selection  has  been  based  is  a  4-week  period,  which  is  a 
longer  period  than  would  ordinarily  be  practicable,  perhaps,  in 
experiment  station  work.  It  is  obvious,  however,  that  with  a 
shorter  period,  the  result  of  physiological  selection  would  be  even 
more  uncertain.  We  are  inclined  to  believe  that  by  far  the  more 
natural  and  satisfactory  procedure  is  to  make  no  physiological  se- 
lection of  animals  whatever,  to  collect  individual  data  wherever 
possible  or  practicable,  and  to  cope  with  the  natural  variability  that 
will  be  found  to  exist  among  the  experimental  results  for  indi- 
viduals within  the  lots  by  the  use  of  statistical  methods.  Any  pro- 
cedure for  reducing  such  variability  that  will  not  deprive  the  ex- 


19^3] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


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534  Bulletin  No.  165  [July, 

periment  of  its  generality  or  its  practical  availability  will  be  of 
value,  of  course,  in  rendering  the  feeding  experiment  more  efficient 
as  an  instrument  of  research. 

(/)  Summary  of  Methods  of  Reducing  Experimental  Error 

We  have  shown  in  this  section  of  the  bulletin  that  according  to 
the  evidence  available  for  study,  the  necessary  precision  in  the 
determination  of  the  relative  fattening  powers  of  two  rations  or 
other  systems  of  treatment  of  farm  animals,  or  of  the  relative  fat- 
tening qualities  of  two  different  lots  of  animals,  not  greatly  dis- 
similar in  character,  is  to  be  obtained  in  several  ways.  It  is  de- 
sirable, first,  to  select  the  experimental  animals  carefully.  If  we 
are  to  determine  the  relative  fattening  value  of  two  rations,  or  two 
methods  of  shelter,  or  of  confinement,  or  of  such  environmental 
factors  as  these,  the  animals  in  both  lots  should  be  of  the  same 
breed  and  type,  sex,  age,  and,  as  far  as  possible,  should  have  been 
under  the  same  treatment  for  some  time  previous.  Disregard  of  such 
requirements  as  these  does  not,  as  might  at  first  be  supposed,  give 
to  the  conclusions  of  the  experiment  a  more  general  applicability, 
but  simply  attaches  to  them  an  additional  and  entirely  avoidable  ele- 
ment of  uncertainty,  for  the  probability  always  exists  that  the  dif- 
ferent breeds,  sexes,  etc.,  react  differently  to  the  experimental  con- 
ditions imposed.  If  we  are  testing  the  fattening  qualities  of  two 
breeds  of  animals,  or  two  lots  at  different  ages,  the  animals  within 
the  lots  should  be  homogeneous  and  the  only  difference  between 
the  lots  should  be  that  of  breeding,  or  age,  i.  e.,  the  factor  under 
investigation. 

In  the  second  place,  the  lots  of  animals  employed  should  be 
fairly  large.  It  seems  unwise  to  use  less  than  lo  or  15  animals  to 
the  lot,  and  wherever  possible  the  lots  should  be  of  more  generous 
proportions,  for  increasing  the  size  of  the  lots  is  the  most  certain 
method  of  rendering  the  conclusions  of  the  experiment  more  sig- 
nificant and  less  ambiguous.  Large  lots  of  animals,  however,  offer 
no  excuse  for  a  poor  selection,  because  the  objections  attendant 
upon  poor  selection  are  not  removed  by  increasing  the  number 
of  animals  experimented  upon,  except  in  so  far  as  one  may  sub- 
divide the  lots  into  larger  and  larger  groups  of  the  requisite  homo- 
geneity. 

In  the  third  place,  the  experiment  may  be  conducted  in  such  a 
way  that  the  experimental  error,  /.  e.,  the  effect  of  individuality  and 
unequal  conditions  within  the  lot,  will  continuously  decrease  and 
the  experiment  will  become  more  and  more  efficient  as  an  instru- 
ment for  the  solution  of  the  problem  at  hand.  We  venture  to  say 
that  this  is  perhaps  one  of  the  most  important  of  the  conclusions  of 


ip/j]  Uncertainty  in  Interpretation  of  Feeding  Exi'ERIMENts  S3S 

this  bulletin,  it  is  universally  conceded  that  the  larger  the  size  of 
the  lots  in  a  feeding'  experiment,  the  better.  Some  investigators, 
at  least,  fully  appreciate  the  fact  that  the  more  homogeneous  the  lots 
as  regards  age,  breed  and  type,  sex,  and  previous  treatment,  the  less 
ambiguous  will  be  the  experimental  results  obtained.  It  is  also  the 
general  opinion  that  within  certain  limits  peculiar  to  the  animals 
under  investigation,  the  longer  the  feeding  period,  the  better  for 
the  solution  of  the  problem  at  hand,  but  this  opinion  is  founded 
upon  the  conviction  that  the  animals  must  become  thoroly  adapted 
to  the  experimental  conditions,  and  not  upon  any  theorem  concern- 
ing the  experimental  error.  Our  results  afford  a  basis  for  the 
general  proposition  that  conditions  favorable  for  fattening  are  fa- 
vorable for  uniform  gains.  In  conducting  feeding  experiments  it 
appears  that  if  experimental  conditions,  such  as  the  prescribed 
rations,  are  constantly  or  increasingly  favorable  to  good  gains,  the 
percentage  variability  of  the  gains  and  the  experimental  error  will 
become  less  and  less. 

Repetition  of  Feeding  Experiments 

Aside  from  the  aliove  method  of  decreasing  the  experimental 
error  in  feeding  trials,  the  necessary  precision  in  the  solution  of 
problems  of  live-stock  raising  may  be  secured  by  the  repetition  of 
experiments  that  by  themselves  do  not  settle  the  point  at  issue.  In 
an  attempt  to  determine,  by  consulting  experiment  station  litera- 
ture, the  efficacy  of  repetition  of  experiments  in  furnishing  con- 
firmatory evidence,  a  striking  condition  of  affairs  and  one  of  vital 
importance,  it  would  seem,  to  experiment  station  work,  was  dis- 
covered. After  reviewing  the  large  amount  of  material  available 
for  such  a  study,  it  was  found  that  frequently  when  the  same  sta- 
tion, and  in  fact  the  same  investigator,  attempted  to  confirm  the 
results  of  previous  experiments  that  apparently  pointed  to  very 
definite  conclusions,  entirely  different  results  were  obtained.  This 
constitutes  no  reproach  or  criticism  against  the  particular  station 
or  investigator  who  thus  failed  to  duplicate  results.  It  does  indi- 
cate, however,  some  defect  in  the  ordinary  method  of  controlling 
the  conditions  in  feeding  experiments,  which  is  worthy  of  investi- 
gation and  remedy. 

Henry's  B.vpcrii)iciits  at  JViscoiisiii  zcith  Pigs. — It  was  with  no 
difficulty  whatever  that  illustrations  of  the  frequent  failure  of  in- 
vestigators to  duplicate  their  own  results  were  found.  We  shall 
first  consider  Henry's  experiments  at  Wisconsin,  extending  over 
ten  years  and  involving  280  pigs.  The  object  of  this  extensive 
investigation  was  to  test  the  value  of  feeding  whole  corn  as  corn- 
pared  with  corn  meal  as  the  main  portion  of  the  ration  for  fatten- 
ing pigs.    Eighteen  feeding  trials  were  performed,  and  in  fourteen 


536 


Bulletin  No.  1G5 


[July, 


of  these  trials  the  corn-meal  lots  made  greater  average  gains  in 
weight  than  the  shelled-corn  lots.  The  percentage  differences  in 
average  gain  in  weight  between  lots  varied  from  31.22  to  0.19,  six 
of  the  trials  exhibiting  percentages  above  20  and  six  below  10. 
The  number  of  pigs  per  lot  in  the  eighteen  trials  is  shown  in  the 
following  table : 


Lots 

Pigs 

Trials 

per  trial 

per  lot 

4 

2 

3 

1 

2 

4 

2 

2 

5 

1 

2 

6 

1 

2 

7 

2 

2 

8 

2 

2 

9 

1 

2 

10 

2 

2 

12 

1 

2 

14 

1 

p 

19 

For  the  experiment  of  1899  on  two  lots  of  19  pigs  each  the 
percentage  difference  between  average  lot  gains  was  0.19  in  favor 
of  the  shelled-corn  lot,  while  in  the  experiment  of  1900  on  two  lots 
of  14  pigs  each  the  percentage  difference  between  average  lot  gains 
was  20.92  in  favor  of  the  corn-meal  lot.  The  average  initial  weight 
of  the  pigs  in  the  latter  trial  was  about  175  lbs.,  and  in  the  former 
trial,  about  186  lbs.  In  the  first  trial,  there  were  10  pure-bred  Po- 
land-Chinas and  28  crossbred  Poland-China-Berkshires,  and  in  the 
second  trial,  21  pure-bred  Poland-Chinas  and  7  crossbred  Poland- 
China-Berkshires,  divided  between  lots  as  equally  as  possible.  The 
first  trial  contained  18  sows  and  20  barrows;  the  second  trial,  11 
sows  and  18  barrows.  The  same  ration  of  ^  shelled  corn  or  corn 
meal  to  ^  wheat  middlings  was  fed  in  both  trials.  The  methods 
of  feeding  the  pigs  were  practically  identical,  the  main  difference, 
apparently,  being  that  in  the  1899  trial  the  shelled  corn  and  mid- 
dlings were  fed  separately  to  Lot  I,  while  in  the  1900  trial  they  were 
fed  together.  The  1899  ^^^^^  extended  over  12  weeks  and  the  1900 
trial  over  14  weeks.  This  brief  comparative  description  of  the 
two  trials  plainly  shows  their  substantial  identity  as  regards  the 
planning  and  execution  of  the  experiment  and  the  known  experi- 
mental conditions  and  does  not  in  the  least  prepare  one  for  the 
widely  divergent  results. 

In  the  first  trial,  the  shelled-corn  lot  gained,  on  an  average, 
1.338  lbs.  per  day,  and  the  corn-meal  lot,  1.336  lbs.  In  the  second 
trial,  the  shelled-corn  lot  gained,  on  an  average,  1. 145  lbs.  per  day, 
while  the  corn-meal  lot  gained  1.4 13  lbs.  An  analysis  of  this  lat- 
ter experiment  by  the  methods  explained  in  Part  I  of  this  bulletin 


jp/j]  Un'CERTAINTY    IX    IXTERPRETATION'   OF    FeEDIXG    ExPERIMEXTS  537 

shows  that  under  the  conditions  of  the  trial  the  odds  are  only  i  in 
about  7700  that  on  repetition  the  shelled-corn  lot  would  give  a 
greater  average  gain  than  the  corn-meal  lot.  The  fact  that  such  a 
contradictory  result  was  obtained  in  the  preceding  year  indicates 
beyond  all  reasonable  doubt  that  for  some  cause  the  tw^o  trials 
were  not  duplicates;  that  is,  that  there  was  some  experimental  con- 
dition or  combination  of  conditions  not  under  control  and  not  de- 
fined, and  yet  oi)erating  in  one  trial  but  not  in  the  other,  or  operat- 
ing very  unequally  in  the  two  trials,  which  created  the  discrepancy 
in  the  results  obtained. 

Further  analysis  of  the  data  of  the  1900  trial  indicates  that  for 
some  reason  which  the  report  does  not  specify,  the  shelled-corn  lot 
ate  considerably  less  corn  and  middlings  than  the  corn-meal  lot. 
Thus,  Lot  I  consumed,  on  an  average,  4.27  lbs.  of  shelled  corn  and 
2.13  lbs.  of  wheat  middlings  per  head  per  day,  while  Lot  II  con- 
sumed 4.51  lbs.  of  shelled  corn  and  2.26  lbs.  of  wheat  middlings. 
In  the  1899  trial,  this  marked  difference  between  lots  did  not  exist, 
Lot  I  consuming  4.44  lbs.  of  shelled  corn  and  2.22  lbs.  of  w'heat 
middlings  per  day,  on  an  average,  and  Lot  II  consuming  4.51  lbs. 
of  com  meal  and  2.25  lbs.  of  wheat  middlings.  Thus,  the  condi- 
tion or  conditions  causing  the  discrepancy  between  these  two  sup- 
posedly duplicate  trials  were  probably  involved  in  the  composition 
or  the  preparation  of  the  rations  fed,  or  possibly  in  the  selection  of 
animals  that  had  been  subjected  to  radically  different  treatment 
just  previous  to  the  experiment. 

Wyoming  Experiments  zdth  Sheep. — In  Bulletins  81  and  85  of 
the  Wyoming  Experiment  Station,  A.  D.  Faville  reports  presum- 
ably duplicate  feeding  trials  undertaken  with  the  idea  of  testing  the 
value  of  Wyoming-grown  grain  for  fattening  sheep.  In  the  first 
test,  performed  in  1908-09,  the  34  sheep  constituting  Lot  III  con- 
sumed, on  an  average,  2.83  lbs.  of  hay  and  0.83  lb.  of  barley  per 
day,  and  made  an  average  daily  gain  in  91  days  of  0.33  lb.  The 
35  sheep  constituting  Lot  I  consumed  2.72  lbs.  of  hay  and  0.81  lb. 
of  corn,  and  made  an  average  daily  gain  of  0.30  lb.  In  the  second 
trial,  performed  the  following  year.  Lot  II,  consisting  of  41  sheep, 
consumed  2.22  lbs.  of  hay  and  0.89  lb.  of  barley  per  day,  and  made 
an  average  daily  gain  of  0.28  lb. ;  while  Lot  I,  also  consisting  of  41 
sheep,  consumed  less  hay  per  day  than  Lot  II,  and  0.89  lb.  of  corn, 
and  made  an  average  daily  gain  of  0.35  lb.  The  average  initial 
weights  of  the  barley  and  corn  lots  in  the  first  trial  were  60.5  and 
59.2  lbs.,  respectively,  and  in  the  second  trial,  64.5  and  63.9  lbs. 
The  sheep  used  in  each  trial  represented  various  breeds,  types, 
and  sizes,  divided  between  lots  as  evenly  as  possible.  The  individ- 
ual data  of  these  experiments  are  not  given  and  a  complete  analy- 
sis is  therefore  impossible.     Assuming,  however,  a  variability  of 


538  Bulletin  No.  165  [July, 

about  21  percent  in  all  lots,  we  find  that  for  the  first  trial  the  odds 
are  I2  to  i  in  favor  of  the  barley  ration,  and,  for  the  second  trial, 
over  100,000  to  I  in  favor  of  the  corn  ration.  In  the  latter  ex- 
periment it  may  be  shown  that  even  if  the  variability  of  the  lots 
were  as  high  as  79.0  percent,  a  value  extremely  improbable,  the  odds 
would  still  be  30  to  i  in  favor  of  the  corn  ration.  We  must  con- 
clude that  this  is  a  second  illustration  of  the  fact^that  the  most 
careful  efforts  to  duplicate  experimental  conditions  in  feeding  ex- 
periments as  they  are  ordinarily  run  often  result  in  failure.^  The 
same  bulletins  offer  a  third  illustration  of  this  fact  in  the  relation 
of  the  barley  to  the  speltz  lots  in  the  two  investigations. 

Montana  Experiments  with  Sheep. — F.  B.  Linfield  reports  sup- 
posedly duplicate  feeding  trials  in  Bulletins  47  and  59  of  the  Mon- 
tana Station,  the  object  being  to  test  the  value  of  local  feeds  in 
fattening  sheep.  In  the  first  experiment,  22  lambs  fed  mixed  grain 
and  clover  hay  made  an  average  daily  gain  of  0.286  lb.  in  95  days, 
and  a  second  lot  of  22  lambs  fed  oats  and  clover  hay  made  an  aver- 
age daily  gain  of  only  0.220  lb.  Again  assuming  a  variability  of 
about  21  percent,  in  the  absence  of  more  definite  information,  the 
odds  are  only  i  to  33,000  that  repetition  would  result  in  a  greater 
gain  for  the  oats  lot  than  for  the  mixed-grain  lot.  With  a  variabil- 
ity as  high  as  46.2  percent,  these  odds  would  still  be  i  to  30.  Nev- 
ertheless, in  the  second  trial,  performed  the  following  year,  24 
lambs  fed  mixed  grain  and  clover  hay  made  an  average  daily  gain 
of  0.231  lb.,  while  an  equal  number  of  lambs  fed  oats  and  clover 
hay  made  an  average  daily  gain  of  0.246  lb.  Other  similar  exam- 
ples occur  in  the  same  two  bulletins,  indicating  the  frequent  inabil- 
ity of  experiment  station  workers  to  duplicate  their  own  experi- 
ments. 

Minnesota  and  Pennsylvania  Experiments  zvith  Steers. — In  Bul- 
letin 76  of  the  ^Minnesota  Station,  Thomas  Shaw  reports  an  in- 
vestigation regarding  the  relative  gains  made  by  steers  while  be- 
ing fattened  during  the  winter  in  the  stall  and  in  an  open  shed. 
The  seven  steers  fed  in  the  barn  made  an  average  daily  gain  of 
1.742  lbs.  per  steer  in  140  days,  while  the  seven  steers  fed  in  the 
open  shed  made  an  average  daily  gain  of  2.256  lbs.  on  the  same 
ration.  In  this  bulletin  the  gains  of  the  individual  steers  are  given, 
and,  applying  biometric  methods,  we  find  that  the  odds  are  1561 
to  I  in  favor  of  out-door  feeding.  Numerous  experiments  per- 
formed  at   the    Pennsylvania   Station,  however,   have   uniformly 

"Concerning  the  second  experiment,  Faville  says :  "The  test  with  barley 
was  hardly  a  fair  one,  as  four  of  the  lambs  in  this  bunch  did  very  poorly.  This 
was  through  no  fault  of  the  grain."  This  explanation  is  hardly  satisfactory, 
since  (1)  poor  gains  by  four  of  the  lambs  would  not  lower  tlie  average  of  41 
gains  to  any  marked  degree,  and  (2)  no  reason  is  given  for  supposing  that 
these  poor  gains  were  not  due  to  the  grain. 


jQij]  Uncertainty  in  Interpretation  of  Feeding  Experiments  539 

failed  to  show  anything  approximating  a  significant  difference  in 
rate  of  gain  between  lots  fattened  in  a  barn  and  lots  fattened  in 
an  open  shed  during  the  winter. 

Difficulties  of  Repetition. — The  illustrations  cited  are  sufficient 
to  show  the  difficulty  of  truly  duplicating  feeding  experiments  as 
ordinarily  planned  and  executed,  that  is,  the  difficulty  of  keeping 
constant,  in  two  consecutive  experiments,  all  conditions  affecting 
to  an  ai)preciable  extent  the  rate  of  growth  of  the  experimental  ani- 
mals. The  conclusion  seems  to  be  that  the  ordinary  manner  of  con- 
ducting such  experiments  contains  some  serious  defect.  How  seri- 
ous the  defect  is  and  how  important  it  is  to  remedy  such  defect  is 
evident  when  one  asks  the  question:  If  the  experimentalist  him- 
self cannot  duplicate  his  own  experiments  and  obtain  similar  re- 
sults even  when  the  most  careful  attention  is  given  to  the  details 
of  management  and  of  experimental  conditions,  what  are  the 
chances  that  the  practical  live-stock  farmer,  who  necessarily  cannot 
duplicate  experimental  conditions  except  in  a  very  approximate 
manner,  will  duplicate  the  results  obtained  by  experiment  stations 
and  profit  by  their  recommendations?  In  many  cases  the  chances 
are  probably  remarkably  small. 

When  such  instances  of  disagreement  between  two  similarly 
conducted  experiments  occur,  the  attempt  is  often  made  to  explain 
away  and  minimize  the  disagreement,  but  the  fact  that  such  disa- 
greements occur  in  spite  of  all  efforts  to  duplicate  experimental 
conditions,  is  significant  and  worthy  of  serious  investigation,  since 
it  is  intimately  concerned  with  the  value  to  the  agricultural  com- 
munity of  all  experiment  station  work  of  the  type  under  discussion. 

A  Probable  Explanation  of  These  Difficulties. — The  conclusion 
to  be  drawn  from  the  occurrence  of  discrepancies  between  sup- 
posedly duplicate  feeding  trials  is  that  the  conditions  deliberately 
imposed  upon  the  experimental  animals  have  not  been  sufficiently 
defined,  so  that  if  a  more  complete  definition  were  made  the  ex- 
planation of  the  discrepancies  would  be  revealed.  It  is  conceivable, 
for  example,  that  the  conclusion  that  barley  has  a  higher  fattening 
value  than  speltz  when  fed  to  lambs  applies  only  when  certain 
grades  of  the  two  grains,  definable,  perhaps,  by  chemical  analysis, 
are  compared. 

It  appears,  therefore,  that  in  formulating  the  conclusions  of  a 
feeding  experiment,  it  must  always  be  borne  in  mind  that  rations 
of  a  definite  chemical  composition,  as  well  as  of  a  definite  qualita- 
tive description,  have  been  compared,  and  that  the  probability  al- 
ways exists  that  if  the  rations  had  been  the  same  as  regard?  quali- 
tative description  but  much  different  as  regards  chemical  composi- 
tion, very  different  results  would  have  been  obtained.  A  chemical 
analysis  of  experimental  rations  may  be  supposed,  therefore,  to 


540  Bulletin  No.  165  [July, 

yield  valuable  if  not  indispensable  data  to  the  proper  appreciation 
of  feeding  experiments. 

Other  conditions  of  the  experiment  should  also  be  clearly  speci- 
fied in  experiment  station  bulletins,  and  the  tendency  to  continually 
generalize  from  data  of  a  very  specific  description  should  be 
guarded  against.  Is  the  experimentalist  in  a  position  to  assert, 
for  instance,  that  his  conclusions  are  not  peculiar  to  the  methods 
of  feeding,  the  times  of  feeding,  the  preparation  of  the  feeds,  the 
mode  of  shelter,  the  extent  of  confinement,  the  breed  of  animals 
experimented  upon,  the  particular  herds  or  localities  from  which  the 
animals  were  drawn,  etc.,  etc.,  which  he  has  employed?  We  ven- 
ture to  suggest  that  such  possibilities  are  worthy  of  consideration, 
and  that  the  determination  as  to  which  of  two  rations  is  the  best 
for  the  fattening  of  animals  is  not  the  simple  problem  that  it  is 
frequently  supposed  to  be. 

Variability  in  the  Composition  oi^  Feedstuffs 

In  connection  with  the  question  of  the  advisability  of  running 
chemical  analyses  on  the  experimental  rations  of  feeding  trials,  it 
was  thought  essential  to  investigate,  if  only  in  a  preliminary  way, 
the  natural  variability  to  which  the  composition  of  some  of  the 
more  common  American  feedstuffs  is  subjected.  For  it  is  of 
course  obvious  that  if  this  variability  is  slight,  so  as  to  be  negligible 
for  all  practical  purposes,  there  is  no  necessity  for  the  analysis  of 
rations  in  each  experiment,  the  average  analyses  compiled  by  the 
Bureau  of  Chemistry,  for  instance,  being  sufficient ;  on  the  other 
hand,  if  this  variability  is  of  such  size  that  it  cannot  properly  be 
disregarded,  then,  for  the  full  appreciation  of  feeding  experiments, 
experimental  rations  must  in  each  case  be  analyzed. 

The  study  of  the  variability  in  the  composition  of  feedstuff's, 
therefore,  is  undoubtedly  of  considerable  importance,  and,  in  view 
of  the  large  mass  of  data  available,  it  could  be  pursued  as  exten- 
sively as  the  most  ardent  statistician  might  desire.  The  statistical 
measures  of  variation  above  developed  are  indispensable  to  such  a 
study.  In  the  preliminary  study  of  this  question  that  has  been 
undertaken  and  that  has  yielded  the  results  briefly  summarized 
below,  these  statistical  constants  have  been  employed.  The  import- 
ance of  a  complete  study  of  the  natural  variability  in  the  composi- 
tion of  American  feedstuffs  is  such  that  it  is  hoped  to  continue  the 
study  later. 

Corn. — Corn  has  long  been  recognized  as  one  of  the  most  stable 
cereals  as  regards  composition.  Thus,  Richardson  says,  speaking 
of  American  corn :  "There  is  apparently  the  same  amount  of  ash, 
oil,  and  albuminoids  in  a  corn  wherever  it  grows,  with  the  excep- 


■fp-fj] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


541 


tion  of  the  Pacific  slope,  where there  seems  to  be  no  facility 

for  obtaining  or  assimilating  nitrogen."^  Hopkins  has  even  doubted 
the  advisability  of  excepting  corn  from  the  Pacific  slope,  with  ap- 
parent justification.^ 

However,  the  statement  above  quoted  may  very  easily  be  mis- 
understood. It  means  simply  that  the  average  analyses  for  corn 
from  the  different  states  of  the  union,  when  compiled  from  a  suf- 
ficient number  of  analyses,  generally  agree  within  narrow  limits. 
For  example,  Richardson  reports  analyses  of  corn  sampled  in  diff- 
ferent  states  from  the  crop  of  1883,*=  The  average  percentages  of 
protein  run  as  follows:  9  samples  from  New  York,  10.54;  20 
samples  from  Illinois,  10.06;  16  samples  from  Minnesota,  10.07; 
15  samples  from  Dakota,  10.75;  ^3  samples  from  Nebraska,  10.47; 
and  II  samples  from  California,  10.26.  The  agreement  is  certainly 
very  close,  considering  the  numbers  of  samples  from  each  state. 

The  statement  that  corn  has  a  very  stable  composition  thus 
means  that  there  are  no  constant  differences  in  its  composition  in 
different  localities  of  the  country.  It  does  not  mean  that  its  com- 
position is  practically  constant  in  any  one  locality.  Thus,  refer- 
ring again  to  Richardson's  analyses,  the  20  samples  of  dent  corn 
from  Illinois  exhibit  a  coefficient  of  variation  of  11.79  ^^  ^^" 
gards  protein  content,  certainly  no  inconsiderable  variability.  Hop- 
kins^ analyzed  three  rows  of  kernels  taken  lengthwise  of  the  ear, 
from  163  ears  of  Burr's  white  corn  grown  on  the  Illinois  Experi- 
ment Station  Farm  in  1896.  The  163  analyses  gave  the  following 
results : 


Ash 

Protein 

10.93 
1.048 
0.58 

Fat 

4.690 
.4232 
9.02 

Carbohydrates 

Average 

Standard  deviation    

Coefficient    of   variation 

1 .  426 

.1090 
7.64 

82.96 
1.182 
1.42 

We  have  determined  the  variability  of  several  groups  of  sam- 
ples of  corn,  each  group  comprising  samples  from  a  single  state 
and  a  single  year's  crop,  tho  not  always  of  a  single  variety  or  even 
of  a  single  class.  As  a  matter  of  fact,  the  differences  in  composi- 
tion between  different  classes  and  varieties  of  corn  (excluding 
sweet  corn  from  consideration)  are  apparently  slight,  judging  from 
the  data  we  have  studied.  From  the  coefficients  of  variation  ob- 
tained in  each  group  of  samples,  we  have  computed  average  co- 

'U.  S.  Dept.  Agr.,  Bur.  Chem.,  Bui.  1,  p.  67.     1883. 
"111.  Agr.  Exp.  Sta.,  Bui.  53,  p.  136.     1898. 
'U.  S.  Dept.  of  Agr.,  Report  for  1884,  pp.  84-85. 
^111.  Agr.  Exp.  Sta.,  Bui.  55,  pp.  208-9.     1899. 


542  .        Bulletin  No.  165  [July, 

efficients,  proper  consideration  being  given  to  the  size  of  the  groups 
in  combining  their  coefficients.^ 

For  protein,  we  have  obtained  an  average  coefficient  of  varia- 
tion of  9.30,  and  for  ash,  an  average  coefficient  of  12.59,  these  two 
coefficients  involving  233  analyses.  The  following  coefficients  in- 
volve analyses  of  154  samples  of  corn:  moisture,  8.94;  fat,  9.22; 
fiber,  16.77;  ^"d  carbohydrate,  1.93. 

The  c[nestion  arises.  How  are  these  coefficients  to  be  inter- 
preted? \A'e  know  roughly  that  the  great  bulk  of  fluctuations  of 
sampling  lie  within  a  range  of  ±3  times  the  standard  deviation 
from  the  mean,^  except  when  the  frequency  distribution  is  of  a 
very  abnormal  type.  It  has  been  our  experience  that  while  the 
distribution  of  percentages  of  the  constituents  of  feeds  is  very  often 
far  from  being  normal,  especially  in  the  case  of  small  percentages, 
such  as  of  fiber  or  ash  in  corn  (see  page  471),  they  are  nevertheless 
not  ordinarily  extremely  asymmetrical,  so  that  we  can  set  the  limits 
of  such  distribution  at  roughly  d=3  times  the  standard  deviation 
from  the  mean.  Thus,  if  the  average  percentage  of  protein  in  a 
year's  crop  in  Illinois,  for  instance,  is  10.50,  the  standard  deviation 
of  samples  taken  thruout  the  state,  as  regards  their  protein  con- 
tent, could  be  estimated  at  9.30  percent  of  10.50,  or  0.976,  and  the 
rough  estimate  may  be  made  that  all  such  samples  would  possess 
protein  contents  ranging  between  10.50+  (3  X  0.976  percent),  i.e., 
between  7.57  and  13.43  percent.  The  extreme  deviations  allowed 
for  by  these  limits,  however,  would  be  of  rare  occurrence,  and  if 
we  are  concerned,  for  instance,  with  the  range  within  which  any 
one  sample  of  corn  would  be  practically  certain  to  fall,  perhaps 
fairer  limits  would  be  ±2.25  times  the  standard  deviation,  that  is, 
between  8.30  and  12.70  percent.  Thus,  if  we  applied  the  average  of 
10.50  percent  of  protein  to  any  one  sample  of  Illinois  corn  for  the 
purpose  of  determining  the  protein  intake  of  a  lot  of  animals  in  a 
feeding  experiment,  we  might  be  in  error  to  the  extent  of  20  to  30 
percent  of  the  total  intake  of  protein,  and  it  may  be  said  without 
exaggeration  that  errors  of  9  to  12  percent  must  be  expected  from 
such  an  approximate  method  of  determining  protein  consumption. 

In  the  case  of  the  ash  intake,  a  still  cruder  approximation  would 
result  from  the  use  of  an  average  percentage,  since  an  error  of  35 
to  40  percent  might  result,  while  errors  of  12  to  15  percent  would 
be  of  relatively  frequent  occurrence.  On  the  other  hand,  an  aver- 
age percentage  of  carbohydrate  could  be  used  with  confidence, 
since,  with  the  most  atypical  sample  of  corn,  an  error  of  more  than 
6  percent  could  hardly  result,  while  the  most  frequent  errors  would 
be  those  of  2  to  3.5  percent. 

"Since  the  standard  deviation  of  the  coefficient  of  variation  decreases  in- 
versely as  the  square  root  of  twice  the  number  of  observations  (see  formula 
on  p.  486),  in  averaging  coefficients  it  was  thought  best  to  weight  each  with^2^ 

"Yule,  "Theory  of  Statistics,"  p.  262. 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  543 

The  question  under  consideration  may  be  approached  from  an- 
other standpoint.  We  have  calculated  the  nutritive  ratios  and  pro- 
duction values  of  6 1  samples  of  flint  corn  grown  in  Connecticut  in 
the  same  year,  the  analyses  of  which  are  given  in  the  Report  of  the 
Connecticut  (New  Haven)  Station  for  1893. 

The  average  nutritive  ratio  was  i :  10.89,  '^"^  ^^^  standard  de- 
viation of  the  second  member  of  the  ratio,  1.398,  or  12.84  percent. 
According  to  the  standard  adopted,  the  limits  of  distribution  may 
be  set  at  the  ratios  i  16.70  and  i  :  15.08.^  Ratios  of  i  :8  or  9,  and 
1:12  or  13  cannot  be  regarded  as  extremely  improbable  of  occur- 
rence. 

The  nutritive  ratio  has  long  been  considered  a  valuable  factor 
in  indicating  the  general  character  of  a  food  and  the  function  it  is 
likely  to  perform  in  a  ration.  The  above  calculations  would  ap- 
pear to  indicate  that  for  corn  this  ratio  is  extremely  variable  for 
different  samples  of  the  grain. 

The  average  production  value  of  the  61  samples  of  Connecticut 
flint  corn  was  89.38  therms  per  100  lbs.  of  grain,  the  standard 
deviation  being  1.348  therms,  or  1.50  percent  of  the  average.  This 
is  a  small  percentage  deviation  and  it  may  therefore  be  concluded 
that,  as  regards  energy  value,  different  samples  of  corn  do  not  vary 
to  any  appreciable  extent,''  or  at  least  to  an  extent  that  cannot 
properly  be  neglected  in  practical  work. 

The  more  important  constituents  of  corn  whose  variability  can- 
not properly  be  neglected  are  the  protein,  ash,  and  moisture.  Con- 
cerning the  latter  constituent,  while  its  variation  in  grains  is  not 
of  any  particular  moment  to  the  nutritive  value  of  the  grain  as 
ordinarily  considered,  it  may,  and  probably  does,  bear  a  close  rela- 
tion to  the  palatability  of  the  grain  for  farm  animals. 

Wheat. — Sharply  contrasted  with  the  stability  in  the  composi- 
tion of  corn  in  different  sections  of  the  country  is  the  extreme 
variability  in  the  composition  of  wheat.  Richardson"^  gives  the 
average  composition  of  wheat  from  different  sections  of  the  coun- 
trv  as  follows : 


"Of  the  61  ratios  actually  calculated,  the  lowest  was  1:S.52,  and  the  highest 
1:15.17,  indicating,  as  would  be  expected  from  the  discussion  on  page  471,  that 
deviations  of  any  given  extreme  magnitude  are  more  frequent  above  the  mean 
than  below,  due  to  the  smallness  of  the  numbers  in  the  second  members  of  the 
ratios  and  to  their  extreme  variability.  The  same  condition  exists  in  the  case 
of  the  distribution  of  percentages  of  crude  fiber,  and  in  a  modified  form,  in 
the  case  of  ash  percentages,  while  percentages  of  protein,  moisture,  and  fat 
exhibit  a  distribtition  more  nearly  approaching  the  normal. 

"Chamberlain's  figures  indicate  that  substantially  the  same  is  true  of  other 
grains.     See  Bui.  120,  Bur.  of  Chem.,  U.  S.  Dept.  of  Agr.    1909. 
"V.  S.  Dept.  Agr.,  Report  for  1884,  p.  77. 


544  Bulletin  No.  165 

Table  25. — Average  Composition  of  American  Wheat 


[July, 


Section 

Number 
of  analyses 

Water 

Ash 

Protein 

Carbo- 
hydrates 

Atlantic  and  Gulf  states 

Middle  states  

Western    states    

Pacific  states    

117 
91 

177 
20 

10.34 

10.61 

9.83 

10.25 

1.77 
1.85 
2.06 
1.87 

11.35 

12.50 

12.74 

9.73 

76.54 
75.04 
75.37 
78.15 

The  variation  in  the  percentage  of  protein  is  very  marked,  and 
is  in  fact  somewhat  obscured  by  considering  such  large  areas  as 
those  in  the  table.  Thus,  Richardson  gives  the  average  protein 
content  of  8  samples  of  Oregon  wheat  as  8.6o  percent,  of  22  sam- 
ples of  North  Carolina  wheat  as  10.43  percent,  of  33  samples  of 
Pennsylvania  wheat  as  11.44  percent,  of  106  samples  of  Colorado 
wheat  as  12.73  percent,  cjf  19  samples  of  Texas  wheat  as  13.14 
percent,  of  13  samples  of  Minnesota  wheat  as  13.19  percent,  and 
of  12  samples  of  Dakota  wheat  as  14.95  percent.^ 

Not  only  does  wheat  ^ary  markedly  in  composition  from  one 
section  of  the  country  to  another,  but  also  from  one  crop  to  the  suc- 
ceeding crop  in  the  same  locality.  The  wheat  investigations  con- 
ducted by  the  Washington  Station  on  the  Washington  crops  of 
1905-09  inclusive  and  reported  in  Bulletins  C4,  91,  and  100  are  of 
interest  in  connection  with  this  point.  Considering  the  Bluestem 
variety  only,  since  this  variety  was  better  represented  than  any  other, 
22  samples  of  the  1905  crop  Q2y:i  an  average  percentage  of  moisture 
of  10.54,  of  protein,  11.79,  ^"^  of  ash,  1.93;  for  the  crop  of  1906, 
represented  by  24  samples,  these  percentages  were  11.25,  13.75,  ^^'^ 
2.18  respectively;  for  30  samples  of  the  crop  of  1907,  10.83,  ii-56, 
and  1.69;  for  22  samples  of  the  crop  of  1908,  9.20,  13.25,  and 
1.88;  and  for  28  samples  of  the  crop  of  1909,  8.1 1,  12.15,  and  1.74. 

From  such  evidence  as  the  above,  it  seems  that  wheat  is  one  of 
the  most  susceptible  of  grains  to  environmental  influences. 

As  regards  the  variability  of  wheat  in  any  one  locality  and  from 
any  one  crop,  we  have  obtained  the  following  average  coefficients 
of  variation  from  data  compiled  by  Richardson :  for  moisture, 
7.10,  involving  242  samples;  for  protein,  9.66,  involving  242  sam- 
ples; for  ash,  11.73,  involving  242  samples;  for  fat,  11.34,  in- 
volving 104  samples;  and  for  fiber,  19.49,  involving  also  104 
samples.  The  coefficients  obtained  for  the  carbohydrate  constitu- 
ents were  comparable  to  those  obtained  for  corn. 

Comparing  these  average  coefficients  with  those  given  above 
for  corn,  it  seems  that  in  the  case  of  the  protein  content  the  two 
grains  are  about  equally  variable;  as  regards  moisture,  wheat  seems 
the  least  variable ;  in  the  case  of  fat,  corn  is  the  least  variable ;  in 

'Tn  this  connection  see  also  Bui.  128,  Bur.  of  Chem.,  U.  S.  Dept.  Agr.,  by 
LeClerc.     1910. 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  545 

the  case  of  ash,  the  difference  is  sHght  and  probably  of  no  signifi- 
cance; and  in  the  case  of  fiber,  both  grains  exhibit  a  high  varia- 
bihty,  testifying  to  the  general  untriistworthiness  of  average  per- 
centages of  fiber  in  grains. 

The  \\'ashingtoii  wheat  investigations  mentioned  above  yield 
coefficients  very  dift'erent  from  those  obtained  from  Richardson's 
data.  Of  the  Washington  analyses,  we  have  considered  only  the 
data  for  the  three  varieties  best  represented,  i.e.,  the  Bluestem, 
Club,  and  Turkey  Red.  Coefficients  of  variation  were  computed 
for  each  variety  for  each  of  the  live  crops  investigated.  The  fif- 
teen coefficients  thus  obtained,  representing  247  analyses,  were 
averaged  together,  each  being  weighted  with  the  square  root  of 
twice  the  number  of  analyses  from  which  it  was  derived  (see  foot- 
note, page  542).  The  fifteen  coefficients  for  the  percentage  of  moist- 
ure averaged  9.88,  and  the  fifteen  coefficients  for  protein,  13.64. 
The  average  coefficient  of  variation  for  moisture  is  thus  almost 
3  percent  higher  than  the  corresponding  average  from  Richard- 
son's data,  while  the  average  coefficient  for  protein  is  almost 
exactly  4  percent  higher  than  the  protein  coefficient  of  Richard- 
son's analyses.  This  would  appear  to  indicate  that  in  Washing- 
ton the  composition  of  wheat  varies  to  a  much  greater  extent 
than  elsewhere.  In  fact,  the  average  coefficient  of  variation  for 
the  protein  content  of  Washington  wheat,  13.64,  is  higher  than 
the  protein  coeffi.cient  obtained  for  any  other  single  state,  the  high- 
est single  coefficient  for  the  other  states  being  12.67,  obtained  from 
61  analyses  of  Colorado  wheat  for  1883. 

From  the  above  study  of  the  variation  to  which  the  composition 
of  wheat  is  subjected  as  its  environment  changes  with  the  locality 
and  the  year  of  growth,  it  is  obvious  that  average  percentages  cov- 
ering the  entire  country,  either  for  one  year's  crop  or  for  several 
combined,  can  have  very  little  if  any  practical  utility,  since  they 
are  not  strictly  applicable  to  the  crop  of  any  one  state  for  any  one 
year,  and  since  they  are  not  even  approximately  applicable  to  the 
crops  of  many  of  the  states.  In  this  respect,  wheat  is  markedly 
different  from  corn,  for  which  average  analyses  seem  to  be  about 
equally  applicable  to  all  sections,  tho,  even  in  the  case  of  corn,  varia- 
tions from  year  to  year  seem  to  occur  and  oftentimes  to  be  of  such 
magnitude  that  they  cannot  properly  be  neglected. 

Considering  only  the  variation  in  the  composition  of  wheat  for 
any  one  state  and  for  any  one  year's  crop,  for  most  sections  of  the 
country  the  evidence  would  seem  to  indicate  that  corn  and  wheat 
are  not  widely  dissimilar,  being  closely  comparable  especially  as 
regards  variation  in  protein  content. 

Grains  in  General. — We  have  made  no  statistical  study  of  grains 
other  than  corn  and  wheat.     However,  of  these  two  corn  seems 


546  Bulletin  No.  105  [July, 

to  be  regarded  as  the  most  stable  and  wheat  as  the  most  labile 
of  the  grains.  From  a  close  inspection  of  the  analyses  collected 
by  Chamberlain  in  Bulletin  120  of  the  Bureau  of  Chemistry,  and 
from  the  data  of  Richardson,  LeClerc,  and  Jenkins  and  Winton,^ 
we  are  inclined  to  believe  that  all  grains  may  be  roughly  charac- 
terized as  follows :  ( 1 )  the  energy  value,  either  total  or  that 
available  for  metabolism  or  that  available  for  fattening,  of  one 
unit  weight  of  dry  substance  of  any  grain  is  approximately  con- 
stant, no  matter  where  or  when  grown;  (2)  with  the  exception  of 
corn,  the  chemical  composition  of  grains  raised  in  different  sections 
of  the  country  varies  decidedly  and  depends,  not  so  much  upon  the 
variety  of  the  grain,  but  upon  the  climatic  conditions  peculiar  to  the 
locality  of  the  crop;  (3)  all  grains  vary  in  composition  from  year  to 
year,  the  extent  of  the  variation  in  composition  seemingly  depend- 
ing upon  the  extent  of  the  variation  in  meteorological  conditions, 
corn  being  apparently  the  least  and  wheat  the  most  susceptible  to 
such  changes;  (4)  the  content  of  moisture,  protein,  and  ash  in 
grains  varies  considerably,  even  in  the  same  locality  and  in  crops 
of  the  same  year,  the  variation  being  such  that  if  the  average 
composition  for  a  given  locality  and  a  given  year  be  applied  to  any 
one  sample  of  grain  for  that  locality  and  year,  an  error  of  10  and 
15  percent  would  not  be  improbable,  while  an  error  of  30  to  40 
percent  would  not  be  impossible. 

Roughages. — We  have  made  no  detailed  study  of  the  variability 
in  the  composition  of  roughages.  Inspection  of  such  data  as  those 
compiled  by  Jenkins  and  \\'inton^  would  seem  to  indicate  that 
roughages  are  much  more  variable  in  composition  than  grains. 
This  is  to  be  expected  when  it  is  recalled  that  with  these  feeds, 
besides  the  climatic  conditions,  the  fertilizers  used,  the  time  of 
cutting,  the  manner  and  time  of  curing,  etc.,  are  probably  of  con- 
siderable importance  in  modifying  the  composition  of  the  feed. 

From  52  analyses  of  commercial  alfalfa  meal  obtained  from 
several  bulletins  on  the  anal3'sis  of  commercial  feedstuffs,^  we 
found  an  average  percentage  of  protein  of  14.83,  a  standard  devia- 
tion of  2.172,  and  a  coefficient  of  variation  of  14.65.  The  latter 
figure  indicates  a  very  considerable  variability,  a  deviation  from 
the  mean  of  44  percent  being  possible,  while  deviations  of  15  to 
25  percent  would  be  of  rather  frequent  occurrence. 

Commercial  Concentrates. — In  obtaining  infonnation  concern- 
ing the  variability  in  composition  of  some  of  the  commoner  com- 

"U.  S.  Dept.  of  Agr.,  Off.  Exp.  Sta.,  Bui.  11.    1892. 

"Bulletins  141  and  152  of  the  Purdue  Station,  Bulletin  141  of  the  Texas 
Station,  Bulletins  316  and  340  of  the  New  York  Station  at  Geneva.  Bulletin 
147  of  the  New  Hampshire  Station,  and  Bulletins  71,  78,  and  120  of  the  Massa- 
chusetts Station. 


19^3] 


Uncertainty  in  Interpretation  of  Feeding  Experiments 


S47 


mercial  concentrated  feedstuffs,  we  have  utilized  the  data  from  a 
large  number  of  bulletins  on  feedstuff  inspection.  The  average 
coefficients  obtained  are  given  in  Table  26. 

Table  26. — Variability  in  the  Composition  of  Commercial  Feedstuffs* 


Feedstuff 


Protein  content 


Number 
of  an- 
alyses 


Average 
varia- 
bility 


Fat  content 


Number 
of  an- 
alyses 


Wheat  bran   

Wheat  middlings  and  shorts. 

Corn  chops  

Cottonseed  meal  or  cake 

Linseed  meal,  old  process.  . . . 

Gluten   feed   

Beef  scraps" 

Beef  scraps" 

Tankage" 

Tankage" 

Blood  meal" 


678 

963 

916 

722 

73 

59 

24 

29 

9 

19 

S 


6.87 
8.97 
8.64 
5.29 
5.74 
10.09 
8.47 
7.05 
6.14 
4.08 
4.25 


352 


711 
73 
59 


Average 
varia- 
bility 


12.01 


18.73 
15.91 
31.84 


Assuming  that  the  distribution  of  the  percentages  of  protein  is 
approximately  normal,  in  appreciating  the  significance  of  the  above 
coefficients  of  variation  the  following  statement  may  be  made :  If 
samples  of  wheat  bran  be  taken  thruout  Illinois,  for  instance,  for 
any  one  year,  and  the  percentage  of  protein  in  each  be  determined, 
I  sample  on  an  average  out  of  every  7  taken  would  exhibit  a  con- 
tent of  protein  at  least  10  percent  greater  or  less  than  the  average 
content  for  all  samples,  and  i  sample  on  an  average  out  of  every 
32  would  exhibit  a  protein  content  at  least  15  percent  removed  from 
the  average  protein  content  for  all  samples.  In  the  case  of  stand- 
ard wheat  middlings  and  shorts,  i  sample  out  of  every  4  would 
give  a  protein  content  10  percent  or  more  on  eitb.er  side  of  the 
mean,  and  i  out  of  every  1 1,  a  content  15  percent  or  more  on  either 
side  of  the  mean.  For  the  other  feedstuffs,  the  following  figures 
would  hold  approximately : 


Feedstuff 


Corn  chops  

Cottonseed  meal 
Linseed  meal   . . . 

Gluten  feed  

Beef  scraps" 

Beef  scraps* 

Tankage" 

Tankage" 

Blood  meal   


Number    of    samples    10 
percent  or  more  greater 
or  less  than  the  mean 


1  out 
1  out 
1  out 
1  out 
1  out 
1  out 
1  out 
1  out 
1    out 


of  every  4 

of  every  17 

of  every  12 

of  every  3 

of  every  4 

of  every  7 

of  every  10 

of  every  70 

of  every  53 


Number    of    samples    15 
percent  or  more  greater 
or  less  than  the  mean 


out  of  every 

12 

out  of  every 

214 

out  of  every 

110 

out  of  every 

8 

out  of  every 

13 

out  of  every 

30 

out  of  every 

68 

out  of  every 

4500 

out  of  every 

2200 

°A11  adulterated  samples  were  left  out  of  the  computations  contained  in  this 
table  when  adulteration  was  noted. 

"Guarantee  of  about  40  percent  protein. 
''Guarantee  of  about  55  percent  protein. 
"Guarantee  of  about  60  percent  protein. 
"Guarantee  of  about  SO  percent  protein. 


548  Bulletin  No.  165  [July, 

From  such  considerations  it  appears  that  if  an  average  analysis 
be  used  in  computing  the  protein  intake  of  experimental  animals 
in  a  feeding  trial,  instead  of  a  direct  analysis,  as  far  as  the  above 
commercial  feeding  stuffs  are  concerned  an  error  of  lo  percent 
or  more  would  not  be  infrequent  in  most  cases,  and  in  some  cases 
an  error  of  even  15  percent  or  more  should  not  occasion  surprise. 

Conclusions. — It  is  evident  from  such  a  preliminary  study  of 
the  question  of  the  variability  in  the  composition  of  American 
feedstuff's,  that  as  regards  feeding  experiments,  the  practical  utility 
of  average  analyses  is  liinitcd,  and  in  the  case  of  many  of  the 
grains  and  roughages  is  small  indeed.  This  conclusion  is  especial!}- 
to  be  emphasized  in  the  case  of  averages  supposed  to  apply  to  the 
entire  country  and  to  all  crops,  since  it  cannot  be  doubted  that 
marked  differences  occur  in  the  composition  of  grains  and  rough- 
ages from  locality  to  locality  and  are  even  likely  to  occur  in  the 
same  locality  in  different  years.  These  remarks  apply,  in  the  case 
of  grains,  to  the  content  of  moisture,  protein,  and  ash  especially; 
while,  in  the  case  of  roughages,  even  the  energy  value  of  a  unit 
weight  of  fresh  substance  may  be  subject  to  marked  variation,  a 
problem  that  we  hope  to  investigate  further.  The  protein  content 
of  commercial  concentrates  is  also  often  subject  to  marked  varia- 
tion. Even  when  averages  are  taken  of  the  composition  of  any 
one  feed  in  any  one  locality  for  any  one  year,  it  has  been  demon- 
strated that  samples  possessing  protein,  ash,  and  moisture  contents 
10  percent,  15  percent,  or  more,  greater  or  less  than  the  mean  con- 
tents, must  be  reckoned  with. 

In  view  of  the  great  variability  in  the  composition  of  feed- 
stufifs  and  of  the  fact  that  a  proximate  analysis  of  rations  can  be 
secured  relatively  easily,  we  are  inclined  to  believe  that  one  cannot 
afford  to  omit  such  a  precaution  in  feeding  experiments,  especially 
when  they  are  otherwise  comprehensively  planned  and  capable  of 
quite  definitely  settling  the  problem  at  hand. 


ipij^    ■    Uncertainty  in  Interpretation  of  Feeding  Experiments  549 

PART  III.    SUMMARY  AND  CONCLUSIONS 

(i)  Difficulties  in  Interpreting  Feeding  Bxperiinents. — The 
simple  feeding  experiment  is  of  value  in  the  solution  of  many  prob- 
lems of  practical  live-stock  raising.  Under  the  best  conditions,  how- 
ever, the  results  of  the  feeding  trial  do  not  point  unequivocally  to 
one  conclusion,  but  are  of  more  or  less  ambiguous  significance. 
The  cause  of  this  ambiguity  is  the  dissimilarity  existing  among  the 
gains  of  individual  animals  due  to  what  may  be  termed  indiznduality 
as  well  as  to  unequal  conditions  within  the  lot  of  animals. 

One  of  the  essential  problems  in  the  interpretation  of  a  feeding 
experiment  is  the  comparison  of  the  gains  in  weight  obtained  for 
one  lot  of  animals  with  the  gains  in  weight  obtained  for  another 
lot,  the  purpose  of  the  comparison  being  to  determine  whether  the 
difference  in  treatment  accorded  the  two  lots,  or  the  difference  in 
their  make-up,  as  the  case  may  be,  has  been  instrumental  in  securing 
a  difference  in  their  gaining  abilities.  If  one  can  assure  himself  by 
the  proper  methods  of  analysis  that  the  relative  position  of  the 
average  gain  of  one  lot  with  respect  to  the  average  gain  of  the 
second  lot  will  remain  essentially  unaltered  if  the  experiment  be 
repeated  on  other  similar  animals  under  similar  conditions,  it  fol- 
lows that  one  is  justified  in  attributing  to  the  essential  difference  or 
differences  in  treatment  or  make-up  between  the  two  lots,  an  influ- 
ence on  their  gaining  qualities.  If  one  cannot  so  assure  himself, 
there  remains  only  the  alternative  conclusion  that  whatever  differ- 
ences in  gains  are  observed  between  the  two  lots  are  due  entirely 
to  the  individualities  of  the  animals  and  to  other  uncontrolled 
factors. 

(2)  The  frequency  Distribution. — One  of  the  most  fruitful 
conceptions  of  the  biometric  method  of  analysis  is  that  of  the  fre- 
quency distribution.  A  set  of  data  obtained  tmder  comparable 
experimental  conditions  is  to  be  thought  of  as  tending  to  assume  a 
definite  distribution  about  some  typical  value,  to  which  value  the 
arithmetic  mean,  or  the  common  average,  is  often  a  good  approxi- 
mation, in  spite  of  the  fact  that  the  sources  of  variation  under  such 
conditions  act  in  a  random  fashion.  It  is  on  this  tendency  of 
comparable  experimental  data  to  assume  a  definite  frequency  dis- 
tribution, expressible  by  a  frequency  curve  capable  of  mathematical 
definition,  that  all  attempts  to  predict  the  result  of  repeating  an 
experiment  must  be  based. 

(3)  Use  of  Average  Results. — Average  results  should  be  used 
with  extreme  caution.  An  average  is  at  best  only  an  imperfect 
description  of  a  series  of  experimental  data,  and  when  used  for 
comparative  purposes  is  often  extremely  misleading.  The  calcu- 
lation of  an  average  should  not  be  considered  a  reason   for  not 


550  Bulletin  No.  165  I      [hdy, 

collecting  or  reporting-  the  original  data,  since  only  by  mi^nce 
to  the  original  data  can  its  value  be  determined,  and  cong^aj^fntly 
only  by  publishing  original  data  can  experiment  station  workers 
criticise  and  properly  appreciate  each  other's  investigations. 

(4)Variatio)i  and  Its  Measurement. — In  adequately  comparing 
the  gains  exhibited  by  one  lot  of  animals  with  those  exhibited  by  a 
second  lot,  it  is  necessary  to  calculate,  not  only  the  average  gain  of 
the  lot,  but  also  the  variation  or  dispersion  of  the  gains  within  the 
lot,  a  measurement  of  the  latter  being  a  measurement  of  the  influ- 
ence of  the  uncontrolled  factors  in  the  experiment.  A  good  meas- 
ure of  variation  for  this  purpose  is  the  standard  deviation,  which 
may  be  defined  as  the  square  root  of  the  average  squared  deviation 
of  all  individual  gains  from  the  average  gain  for  the  lot. 

The  average  of  a  series  of  gains  in  weight,  as  well  as  the  in- 
dividual gains,  must  be  considered  as  possessing  a  variability  due  to 
the  experimental  factors  that  were  not  under  control,  and  since 
these  uncontrolled  factors  find  direct  expression  in  the  variability 
of  gains  within  the  lot,  it  follows  that  the  variability  of  an  average 
gain  bears  a  definite  relation  to  the  variability  of  the  individual 
gains  within  the  lot.  Obviously,  the  variability  of  an  average 
gain  decreases  as  the  size  of  the  lot  increases,  and  it  may  be  shown 
that  the  relation  is  such  that  the  presumptive  standard  deviation  of 
the  average  gain  is  equal  to  the  standard  deviation  -of  the  original 
gains  divided  by  the  square  root  of  their  number. 

(5)  The  Probable  Error. — In  predicting  the  result  of  repeating 
a  feeding  experiment,  on  two  lots  of  animals  w^e  will  say,  using 
other  animals,  but  subjecting  them  to  the  same  conditions  that 
obtained  in  the  given  experiment,  we  first  make  the  assertion  that 
the  most  probable  average  lot  gains  that  would  be  obtained  in  a 
second  experiment  are  the  average  lot  gains  actually  obtained  in 
the^first  experiment.  Our  prediction  is  very  inadequate,  however, 
until  we  estimate  from  the  data  of  the  first  experiment  what  devia- 
tions in  a  second  experiment  we  must  expect  from  these  most 
probable  values,  since  it  would  be  remarkable  indeed  if  exact  dupli- 
cation occurred.  It  is  the  purpose  of  the  probable  error  of  these 
average  lot  gains  to  afford  this  information. 

The  probable  error  of  an  average  gain  is  that  value  which,  w^hen 
added  to  and  subtracted  from  the  average,  defines  two  limiting 
values  such  that  the  odds  are  .even  that  a  second  experiment  will 
give  an  average  gain  falling  between  them.  If  w^e  add  to  and 
subtract  from  an  average  gain  3.17  times  its  probable  error,  there 
are  obtained  two  limiting  values  such  that  the  odds  are  30  to  i 
that  a  second  experiment  will  give  an  average  falling  between  them. 
Now  odds  of  30  to  I  represent  a  degree  of  confidence  amounting 
to  practical  certainty,  so  that  we  may  feel  reasonably  certain  that 


ipij]  Uncektainty  in  Interpretation  of  Feeding  Experiments  551 

a  second  experiment  will  give  an  average  gain  for  a  lot  of  animals 
of  a  specified  description  and  under  specified  conditions,  lying 
somewhere  within  an  interval  defined  by  adding  to  or  subtracting 
from  the  average  gain  experimentally  obtained  3.17  times  its  prob- 
able error.  The  probable  error  of  an  average  gain  is  obtained  by 
simply  multiplying  the  standard  deviation  of  the  average  by  0.6745. 

It  is  generally  desired,  however,  to  determine  the  significance 
not  only  of  average  lot  gains,  but  also  of  differences  between  aver- 
age lot  gains.  The  probable  error  of  such  a  difference  may  then 
be  calculated  by  squaring  the  probable  errors  of  the  two  averages 
involved,  adding,  and  extracting  the  square  root  of  the  sum.  The 
probable  error  of  a  difference  between  two  average  gains  defines 
its  significance  in  exactly  the  same  manner  as  the  probable  error 
of  an  average  gain  defines  the  significance  of  that  average. 

By  the  use  of  such  a  probability  method  as  that  briefly  out- 
lined above,  we  are  able  to  interpret  the  results  of  feeding  experi- 
ments in  a  fairly  satisfactory  manner.  The  element  of  uncertainty 
resulting  from  the  meaningless  variation  existing  among  individual 
gains,  due  to  uncontrolled  experimental  factors,  has  been  definitely 
and  reasonably  defined. 

(6)  CoefHciciits  of  Variation. — For  some  purposes,  the  stand- 
ard deviation  is  inadequate  as  a  measure  of  variation,  due  to  the 
fact  that  it  depends  upon  the  units  of  measurement  employed,  and 
for  gains  obtained  during  different  periods  of  time  or  gains  ex- 
hibited by  different  kinds  of  animals,  is  correlated  with  the  aver- 
age gain.  For  extensive  comparisons  of  variation,  therefore,  the 
coefficient  of  variation  is  used,  this  coefficient  being  simply  the 
standard  deviation  calculated  as  a  percentage  of  the  average.  The 
coefficient  of  variation  of  gains  within  lots  is  a  good  measure  of 
the  experimental  error. 

From  an  extensive  review  of  experiment  station  literature  in 
this  country,  we  have  obtained  an  average  coefficient  of  variation 
of  gains  of  about  21  for  similarly  treated  lots  of  sheep.  For 
steers  and  swine,  an  average  coefficient  of  about  17  has  been  ob- 
tained. From  these  figures,  supplemented  by  a  detailed  study  of 
the  data,  it  appears  probable  that  sheep  in  general  exhibit  greater 
variability  in  gaining  qualities  than  do  either  steers  or  swane.  The-, 
small  amount  of  data  we  have  collected  concerning  the  fattening 
of  poultry  indicate  an  average  variability  of  about  16  percent. 
Apparently  poultry  may  be  classed  with  steers  and  swine  as  re- 
gards variability  of  gains. 

Extreme  discrepancies  were  found  to  exist  among  individual 
coefficients  of  variation.  This  is  doubtless  due  in  part  to  the  het- 
erogeneity of  the  data,  but  it  is  in  large  part  to  be  expected  from  the 
mere  size  of  the  coefficients.  A  determination  of  a  relation  be- 
tween particular  rations  or  systems  of  treatment  and  the  variability 


1 


SS2  Bulletin  No.  165  [July, 

of  gains  is  practically  impossible  except  in  extensive  or  in  repeated 
experiments.  • 

(7)  Number  of  Animals  Required  per  Lot. — Based  upon  the 
average  coefficients  of  variation  found  for  sheep  and  for  steers 
and  swine,  calculation  indicates  that  experimental  lots  should  con- 
tain at  least  10  to  14  animals,  or  even  25  to  30  animals  wh^i  the 
rations  or  other  conditions  under  investigation  are  very  similar. 
The  necessity  of  using  at  least  10  to  15  animals  per  lot  in  feeding 
trials  seems  to  be  well  established.  Wherever  this  number  can  be 
increased,  the  better,  for  this  is  the  surest  and  most  generally  rec- 
ognized means  of  increasing  the  significance  of  experimental  re- 
sults. Again,  however,  it  is  well  to  note  that  increasing  the  size 
of  lots  is  no  remedy  for  a  poor  selection  of  experimental  animals. 
Furthermore,  increasing  the  size  of  lots  cannot  eliminate  individ- 
uality, but  merely  reduces  its  effect  on  the  average.  It  has  been 
shown  that  when  there  are  as  many  as  40  animals  to  the  lot,  an 
appreciable  degree  of  uncertainty  still  attaches  to  average  lot  gains. 
Also  it  should  be  borne  in  mind  that  the  beneficial  effect  of  increas- 
ing the  size  of  lots  varies  not  with  the  number  in  the  lot,  but  with 
the  square  root  of  this  number.  Thus,  for  the  same  standard 
deviation  of  individual  gains,  a  lot  of  10  animals  will  give  a  prob- 
able error  of  the  average  gain  only  twice  as  large  as  a  lot  of  40 
animals. 

(8)  Uniformity  of  Gains  is  Desirable. — Whenever  and  where- 
ever  possible  it  is  advantageous  to  reduce  the  experimental  error 
of  feeding  trials,  i.e.,  to  increase  the  uniformity  of  gains  within 
the  lots,  provided  the  value  of  the  experiment  and  its  practical 
availability  are  not  also  thereby  reduced.  The  smaller  the  coeffi- 
cient of  variation  of  the  gains  in  weight  within  a  lot,  other  things 
being  equal,  the  smaller  the  minimum  percentage  difference  be- 
tween its  average  gain  and  that  for  a  second  lot  that  can  be  defi- 
nitely traced  to  the  difference  in  treatment  or  to  the  difference  in 
make-up  between  the  two  lots.  Hence  a  reduction  of  the  experi- 
mental error  means  a  reduction  in  the  coefficient  of  variation  of 
gains  within  the  lots. 

(9)  Selection  of  Animals  to  Insure  Uniformity  of  Gains. — 
It  is  well  known  that  animals  at  different  ages  exhibit  different 
rates  of  growth  and  different  fattening  qualities.  It  is  also  obvious 
that  different  breeds  of  the  same  species  of  animals  often  exhibit 
similar  differences,  especially  if  they  are  of  different  general  types, 
and  even  where  it  is  not  obvious  that  breed  differences  exist  it  is  not 
justifiable  to  assume  that  they  do  not  exist.  The  available  data 
indicate  with  a  high  degree  of  certainty  that  wethers  gain  faster 
than  ewes,  barrows  faster  than  sows,  and  cockerels  faster  than 
pullets,  at  least  at  the  fattening  age.  Furthermore,  it  is  beyond 
dispute  that  differences  in  treatment  of  animals  previous  to  ex- 


/p/j]  UXCERTAIXTV   XX    IXTERPRETATION  OF  FEEDING   EXPERIMENTS  SS3 

periment  may  frequently  be  the  cause  of  differences  in  fattening 
qualities.  The  careful  and  intelligent  selection  of  the  experimental 
animals  is  one  of  the  best  methods  of  reducing  the  experimental 
error  and  thus  obtaining  more  valuable  and  more  significant  re- 
sults without  interfering  with  conditions  that  the  experiment  must 
conform  to  by  reason  of  the  use  to  which  its  conclusions  are  to 
be  put.  We  cannot  over-emphasize  the  necessity  of  securing  per- 
fectly homogeneous  lots  as  regards  age,  breed,  type,  sex,  and  pre- 
vious treatment.  The  great  preponderance  of  evidence  indicates 
that  by  thus  selecting  the  animals  for  experimental  purposes,  the 
experimental  error  will  be  greatly  reduced.  The  necessity  of 
selecting  homogeneous  lots  of  animals  is  not  appreciably  dimin- 
ished by  the  balancing  of  heterogeneous  lots. 

(lo)  Good  Gai)is  are  Unifonn  Gains. — In  ^ny  experiment  in- 
\T)lving  two  or  more  lots  of  animals,  it  has  in  general  been  found 
that  the  lots  exhibiting  the  best  average  gains  also  exhibit  the 
more  unifonn  "gains,  and  vice  versa. 

(ii)  Changes  in  the  Variability  of  Gains  During  an  Experi- 
ment.— It  has  been  found  from  experiments  in  which  the  ex- 
perimental animals  have  been  weighed  periodically  during  the 
investigation  that  frequently  the  coefficient  of  variation  of  gains 
progressively  decreases  from  the  l^eginning  q|  the  experiment  to 
the  end,  the  rate  of  decrease  being  greater  during  the  early  periods 
than  during  the  later  periods  of  the  feeding  trial.  Apparently  this 
decrease  would  not,  under  the  best  conditions,  continue  indefi- 
nitely, but  would  gradually  attain  to  a  minimum  coefficient  char- 
acteristic of  the  particular  sample  of  animals  under  observation 
and  of  the  particular  experimental  conditions. 

In  other  experiments,  a  continuous  decrease  in  the  coefficient 
of  variation  of  gains  is  not  evident.  In  most  cases  of  this  descrip- 
tion that  we  hav6  analyzed,  a  more  or  less  close  correlation  be- 
tween changes  in  ration  and  changes  in  variability  of  gains  may 
be  observed,  such  that  an  increasing  ration  is  generally  accom- 
panied by  a  decreasing  coefficient  of  variation,  a  constant  ration 
by  a  constant  or  slightly  increasing  coefficient,  and  a  decreasing 
ration  by  an  increasing  coefficient.  Unfavorable  weather  condi- 
tions seem  also  to  be  instrumental  in  producing  more  variable 
gains,  while  in  a  few  instances  the  correlation  between  ration  and 
coefficient  of  variation  above  defined  seems  to  be  complicated  or 
obscured  by  other  factors,  such  as  the  relation  of  food  intake  to 
body  weight  or  bodily  requirements.  \\'hile  the  evidence  adduced 
does  not  unanimously  point  to  one  explanation  of  the  changes  in 
variability  of  gains  during  the  course  of  a  feeding  trial,  consider- 
able support  may  be  found  for  the  general  statement  that  when 
conditions  are  constantly  or  increasingly  favorable  to  growth  and 


554  Bulletin  No.  165  [July, 

fattening,  an  increasing  uniformity  of  gains  is  generally  secured, 
or  in  other  words,  the  experimental  error  is  progressively  reduced. 
It  seems,  therefore,  that  whenever  practicable  and  whenever  the 
nature  of  the  experiment  will  permit,  the  animals  should  be  in- 
duced to  consume  an  increasing  amount  of  food,  that  is,  a  con- 
stant ration  per  lOO  lbs.  live  weight.  A  considerable  increase 
in  the  ration  near  the  close  of  the  experiment  for  the  purpose  of 
"finishing  off"  the  animals  for  the  market  is  frec[uently  very  effi- 
cacious in  securing  more  uniform  gains. 

(12)  Physiological  Selection. — Another  method  of  reducing 
the  experimental  error  of  feeding  trials  that  is  in  vogue  in  one 
form  or  another  at  different  stations,  has  been  investigated.  The  es- 
sence of  this  method  is  the  selection  for  experiment  of  only  those 
animals  that  during* the  course  of  a  preliminary  feeding  period  have 
proved  themselves  to  be  functionally  similar  as  regards  the  rate 
of  growth  or  fattening".  Hence  we  have  called  the  method  physi- 
ological selection.  From  theoretical  considerations  alone,  it  appears 
that  even  if  physiological  selection  is  efficacious  in  accomplishing 
its  purpose  of  eliminating  poor  gainers  and  reducing  experimental 
error,  it  will  so  multilate  the  feeding  experiment  itself  as  to  render 
it  much  less  valuable  to  practical  li\"e-stock  farming  and  to  limit 
its  applicability  and  thus  reduce  its  significance. 

Experimental  evidence,  however,  indicates  clearly  that  physi- 
ological selection  does  not  eliminate  the  poor  gainers.  In  fact^it 
appears  that  those  animals  exhibiting  the  poorest  gains  in  a  pre- 
liminary period  are  in  general  no  worse  than  a  random  sample  of 
the  entire  group  of  animals  in  a  subsequent  feeding  experiment. 
Furthermore,  physiological  selection  is  very  inefficient  in  reducing 
experimental  error,  even  when  conducted  along  the  most  rigorous 
lines.  Hence  this  method  is  both  theoretically  faulty  and  practi- 
cally incompetent  to  accomplish  its  purposes. 

(13)  Repetition  of  E.vpcriuients. — The  necessary  precision  in 
feeding  trials  may  be  attained  by  a  reduction  of  the  experimental 
error  as  above  shown  or  by  repetition  of  the  experiment.  From 
a  study  of  the  efficacy  of  repetition,  it  appears  that  frequently 
under  the  most  favorable  conditions,  feeding  experiments  cannot 
be  duplicated.  Frequently  experiment  stations  have  obtained  re- 
sults from  feeding  trials  pointing  unequivocally  to  a  certain  con- 
clusion, and  yet  subsequent  attempts  to  duplicate  such  experiments 
have  yielded  results  quite  incompatible  with  the  first  conclusion. 
The  gravity  of  such  a  situation  cannot  be  over-emphasized.  Its 
remedy  seems  to  be,  first,  the  more  careful  reporting  of  experimental 
conditions,  including  a  chemical  analysis  of  rations,  and  second,  the 
conviction  that  the  conclusions  of  feeding  experiments  are  more 
intimately    connected   with  the  particular   experimental  conditions 


ip/j]  UXLEKTAINTV    IN    INTERPRETATION    OF    FEEDING    EXPERIMENTS  555 

that  obtained  than  has  heretofore  been  beheved.  The  conckision, 
for  instance,  that  one  feed  is  better  for  fattening  purposes  than 
another  may  be  totally  at  fault  if  other  samples  of  the  two  feeds, 
possessing  quite  different  compositions,  be  used,  or  if  other  breeds 
of  animals,  or  animals  more  (or  less)  mature,  be  used,  or  other 
methods  of  preparing  the  feeds  or  sheltering  the  animals  be  fol- 
lowed. Such  possibilities  should  always  be  kept  in  mind,  and  the 
frequent  tendency  to  generalize  from  data  of  a  very  specific  de- 
scription should  be  carefully  guarded  against. 

(14)  Variability  in  the  Composition  of  Feedstuff s. — The  ad- 
visability of  submitting  experimental  rations  to  a  chemical  analy- 
sis is  clearly  indicated  by  a  study  of  the  variability  in  the  composi- 
tion of  feedstuffs.  In  the  case  of  grains,  this  varialnlity  is 
negligible,  apparently,  as  far  as  the  energy  value  of  the  feed  is 
concerned,  but  it  is  considerable  and  in  many  cases  extreme  in  the 
case  of  the  moisture,  protein,  and  ash  content.  With  roughages, 
inspection  of  analytical  data  w^ould  indicate  an  even  greater  vari- 
ability than  with  grains,  apparently  involving  even  the  energy 
value.  In  the  case  of  commercial  concentrates,  variation  of  the 
protein  content  is  often  quite  comparable  to  that  in  grains,  tho  in 
the  more  highly  nitrogenous  concentrates,  such  as  blood  meal  with 
a  protein  guarantee  of  80  percent,  the  percentage  variability  is 
less  evident. 

(15)  Individual  Feeding  Not  Essential. — The  simple  feeding 
experiment  concerning  itself  entirely  with  the  gains  in  weight 
and  the  feed  consumption  of  farm  animals  under  certain  definite 
experimental  conditions,  has  served  many  useful  purposes  and 
yielded  much  valuable  information  to  practical  live-stock  farming. 
Its  purpose  is  to  yield  specific  information  which  must  generally  be 
considered  in  connection  with  the  specific  conditions  under  which  it 
was  conducted,  as  opposed,  for  instance,  to  the  purpose  of  the 
nutrition  experiment,  which  is  the  securing  of  more  or  less  general 
information,  not  so  strictly  limited  by  the  conditions  under  which 
the  experimental  data  were  collected.  Therefore,  it  is  neither 
necessary  nor,  in  fact,  expedient  that  the  technic  of  the  simple 
feeding  experiment  be  carried  to  the  same  degree  of  refinement  as 
that  of  the  nutrition  experiment  proper.  Any  great  refinement  of 
the  former,  is  objectionable  from  the  standpoint  of  the  practical 
availability  of  the  results  of  feeding  trials. 

Thus,  the  individual  feeding  of  animals  in  ordinary  feeding  trials 
seems  unnecessary,  if  not  inadvisable,  because  we  are  here  imposing 
an  experimental  condition  entirely  out  of  harmony  with  ordinary 
practical  live-stock  raising,  and  while  the  experimental  error  may 
very  probably  be  reduced  by  seeing  to  it  that  each  animal  obtains 
the  same  amount  of  feed  per  100  lbs.  live  weight  for    instance, 


SS6  Bulletin  No.  165  [July, 

the  practical  availability  of  the  experimental  data  obtained  would 
undoubtedly  be  greatly  reduced.  The  individual  feeding  of  ani- 
mals may  yield  valuable  data  for  some  purposes.  However,  the 
variability  in  the  consumption  of  feed  and  consequently  in  the 
gains  produced  cannot  be  presumed  to  be  the  same  in  individual 
feeding  as  in  lot  feeding. 

(i6)  Publication  of  Results.' — The  results  of  feeding  experi- 
ments should  be  published,  not  only  with  the  idea  of  describing  a 
particular  investigation,  but  also  with  the  idea  of  determining,  in 
so  far  as  such  a  determination  is  possible,  whether  a  reasonable 
probability  exists  that  the  practical  live-stock  farmer  will  actually 
benefit  himself  by  applying  the  results  of  the  investigation  to  his 
own  live  stock.  If  no  such  probability  exists,  the  farmer  should 
be  specifically  warned.  The  elaborate  analysis  necessary  for  an- 
swering such  a  question  will  very  probably  not  be  appreciated  by  the 
majority  of  the  readers  of  experiment  station  bulletins,  but  this 
is  no  excuse  for  not  using  such  analytical  methods  at  the  expense 
of  accuracy  in  the  formulation  of  conclusions  and  recommenda- 
tions. As  a  matter  of  fact,  the  analysis  undertaken  need  consti- 
tute no  part  of  the  bulletin  published,  the  purpose  of  such  analysis 
being  primarily  simply  to  check  or  rectify  conclusions. 

(17)  Formulating  Conclusions. — In  formulating  the  conclu- 
sions of  feeding  experiments,  the  necessity  of  keeping  in  mind  the 
possibility  that  several  of  the  specific  experimental  conditions  may 
seriously  limit  the  applicability  of  the  results  of  the  investigation 
should  not  be  lost  sight  of.  Thus,  Ration  A  may  be  superior  to 
Ration  B  under  some,  but  not  all,  conditions.  The  possibility,  if 
not  the  probability,  exists  that  if  the  constituents  of  Ration  A  are 
not  up  to  a  certain  standard,  the  reverse  relation  may  hold ;  hence 
the  necessity  of  a  chemical  analysis  of  the  rations  used  in  order 
that  one  may  know  the  actual  conditions  under  which  the  experi- 
mental conclusions  may  reasonably  be  applied.  It  is  not  sufficient 
simply  to  enumerate  the  individual  feeds  of  which  the  rations  are 
constituted  and  the  proportions  in  which  they  enter  into  the  ra- 
tions. An  exhaustive  and  repeated  chemical  anlysis  of  rations  is 
neither  necessary  nor  especially  advantageous.  In  fact,  if  a  fairly 
complete  analysis  of  feeds  be  made  at  the  beginning  of  the  experi- 
ment and  substantially  the  same  feeds  be  used  thruout  the  subse- 
quent feeding  period,  it  may  be  necessary  to  run  only  moisture 
determinations  on  the  feeds  from  time  to  time  during  the  experi- 
ment. If  variation  in  the  moisture  content  of  feeds  is  not  appre- 
ciable during  storage,  even  the  repetition  of  moisture  determina- 
tions will  be  unnecessary.  However,  an  ordinary'  analysis  should 
be  made  of  each  new  supply  of  feed  from  a  sample  fairly  repre- 
sentative of  the  entire  supply. 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  557 

Other  conditions  than  the  composition  of  rations  may  limit  the 
appHcabihty  of  conchisions.  The  manner  in  which  the  feeds  are 
given  to  the  animals,  e.g.,  whether  they  be  given  ad  libitimi  or  in 
restricted  quantities,  may  determine  to  some  extent  the  relative 
merits  of  rations.  The  breed  or  type  of  animals  experimented 
upon  may  be  still  another  limiting  factor.  The  age  or  condition 
of  the  animals  may  be  still  other  limiting  factors.  Such  consid- 
erations as  these,  which  are  associated  with  greater  or  less  degrees 
of  probability,  should  receive  due  attention  in  interpreting  feeding 
experiments,  and  the  assertion  that  a  given  experiment  indicates 
a  superiority  of  one  ration  over  another  should  be  made  only  in 
close  connection  with  a  brief  statement  of  the  more  important  ex- 
perimental conditions. 

In  conclusion,  we  take  pleasure  in  acknowledging  the  valuable 
assistance  of  Professor  H.  L-  Rietz  in  aiding  us  to  a  proper  com- 
prehension of  the  technic  of  the  statistical  methods  and  of  their 
general  applicability  to  agricultural  problems. 


SS8 


Bulletin  No.  165 


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Uncertainty  in  Interpretation  of  Feeding  Experiments 


569 


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19^3]  L'XCERTAIXTY    IN    INTERPRETATION    OF    FEEDING    EXPERIMENTS  571 


Number  of  Animals  to  Include  in  an  Experimental  Lot 

Two  equal  lots  of  animals  of  a  given  species  are  fed  according 
to  two  different  methods  or  treated  otherwise  in  a  distinctive 
fashion.^  After  a  feeding  period  of  a  given  length,  Lot  I  ex- 
hibits an  average  gain  of  a  lbs.,  and  Lot  II  an  average  gain  of 
b  lbs.  The  coefficient  of  variation  of  the  gains  in  Lot  I  we  shall 
call  Cj,  and  that  of  Lot  II,  C2.  Therefore,  the  best  estimates  of 
the  standard  deviations  of  the  two  average  gains  in  weight  are 

respectively,  ^-.^\—  ,  and    Vnn^  /— »  *^   being  the  number  of  ani- 

mals  in  the  lots.  Now,  let  the  percentage  difference  between  the 
two  average  lot  gains  a  and  b  be  designated  by  the  letter  c  (or 
rather,  by  cXiOO),  that  is,  let 

This  being  so,  it  follows  that 

,        2 — c     ^  J    .       J.         2  a  c 

The  standard  deviation  of  the  dift'erence  (a — b)  is  equal  to  the 
square  root  of  the  sum  of  the  squares  of  the  standard  deviations 
of  a  and  b,  or,  denoting  this  standard  deviation  by  Cab 

Substituting  the  value  of  b  in  terms  of  a  and  c  above  found, 

The  ratio  of  tlie  dift'erence   {a — b)   to  its  standard  deviation  is 
therefore 

a— I  _2ac         ^  j~      __r2  — n-'  ^c  X  100 

Qa-b  ^  2-\-c  '^  100 


a /  r2  —  ry  _  2c  X  100  yn 


Now,  in  order  that  the  odds  be  at  least  30  to  i  that  the  difference 
(a — b)  is  significant  in  the  sense  that  it  is  in  part  due  to  the  differ- 
ence in  the  treatment  accorded  Lots  I  and  IL^'this  ratio  of  (a — b) 
to  the  presumptive  standard  deviation  of  (a — b)  must  be  at  least 
equal  to  1.849,  '^  number  obtainable  from  a  table  of  the  values 
of  the  normal  probability  integral,  such  as  that  in  C.  B.  Daven- 

*The  following  discussion  will  also,  of  course,  apply  to  two  equal  lots  of 
animals  of  different  type,  breed,  age,  sex,  etc.,  treated  similarly. 

''Or,  in  the  case  of  dissimilar  lots  treated  alike,  to  the  difference  in  breed, 
type,  age,  sex,  previous  treatment,  etc.,  between  Lots  I  and  II. 


572  Bulletin  No.  165  [July, 

port's  "Statistical  Methods,"  2d  cd.,  p.   119.     Therefore,  by  solv- 
ing the  equation 

2  Cx  100  i/TT 


Vcii'z-\-cy-{-ci{'Z-cy 


=1.849 


for  71,  assigning  different  values  to  c  and  the  most  probable  values 
available  for  Cj  and  Co,  we  obtain  an  estimate  of  the  least  number 
of  animals  per  lot  that  can  be  used  in  satisfactorily  demonstrating 
the  significance  of  the  corresponding  percentage  difference  c. 
For  the  use  to  which  the  above  formula  is  to  be  put,  we  shall 
simplify  the  problem  by  assuming  that  Ci^C2  =  C.  The  formula 
to  be  solved  for  11  then  reduces  to 

fX'^""^^^  1.849,  or  „  =  ri-8«Cl/2+li?1' 

In  constructing  Table  i,  page  487,  the  values  assigned  to  C 
are  21  for  sheep  and  17  for  swine  and  steers,  these  values  being 
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Bibliography 


1.  Craig,  S.  J.  and  Melvin,  L.  R.  III.  Agr.  Exp.  Sta.   Bachelor  Thesis.  1906. 

2.  Craig,  J.  A.  Wis.  Agr.  Exp.   Sta.  Bui.  32.     1892. 

3.  Coffey,  W.  C.  111.  Agr.  Exp.  Sta.  Bachelor  Thesis.    1906. 

4.  Wilson,  J.  W.  So.  Dak.  Agr.  Exp.  Bui.  119.    1910. 

5.  Wilson,  J.  W.  Ibid. 

6.  Coffey,  W.  C.  111.  Agr.  Exp.  Sta.  Master  Thesis.    1909. 

7.  Chilcott,   E.  C.  and  Thornber,  W  T.  So.  Dak.  Agr.  Exp.  Sta.  Bui.  71. 

1901. 

8.  Carlyle,  W.  L.  Wis.  Agr.   Exp.  Sta.  16th  Annual  Report.    1899. 

9.  Carlyle,    W.    L.   Wis.   Agr.   Exp.    St^.   15th  Annual   Report.    1898. 

10.  Craig,  J.  A.  W'is.  Agr.   Exp.  Sta.   Bui.   32.     1892. 

11.  Wilson,  J.  W.  and  Skinner,  H.  G.  So.  Dak.  Agr.  Exp.  Sta.  Bui.  86.  1904. 

12.  Wilson,  J.  W.  and  Skinner,  H.  G.  So.  Dak.  Agr.  Exp.  Sta.  Bui.  80.  1903. 

13.  Mumford,  H.  W.  Mich.  Agr.  Exp.  Sta.  Bui.  136.    1896. 

14.  Arkell,  T.   R.  N.  H.   Agr,  Exp.   Sta.   Bui.   152.    1911. 

15.  Arkell,  T.  R.  Ibid. 

16.  Grindley,  H.  S.,  Coffey,  W.  C,  and   Emmett,  A.   D.  111.  Agr.  Exp.  Sta. 

Unpublished  manuscript.    1912. 

17.  Voelcker,  J.  A.  Journ.  Roy.  Agr.   Soc.  of  Engl.  Vol.   63.    1902.     From 

Woburn  Station. 

18.  Voelcker,  J.  A.  Journ.   Roy.  Agr.   Soc.  of  Engl.  Vol.   62.    1901.     From 

Woburn  Station. 

19.  Voelcker,  J.  A.  Journ.  Roy,  Agr,  Soc.  of  Engl,  Vol.  60.    1899.     From 

Woburn  Station. 

20.  Voelcker,  J.  A,  Ibid. 

21.  Voelcker,  J.   A.  Journ.  Roy.  Agr.   Soc.  of  Engl.   Vol.   59.    1898.     From 

Woburn   Station. 

22.  Voelcker,   J.  A.  Journ.  Roy.  Agr.  Soc.   of  Engl.  Vol.  57.    1896.     From 

Woburn  Station. 

23.  Voelcker,  J.  A.  Journ.  Roy.  Agr.  Soc.   of  Engl.  Vol.  53.    1892.     From 

Woburn  Station. 

24.  Voelcker,  J.  A.  Journ.  Roy,  Agr.  Soc.   of  Engl.  Vol.  56.    1895. 

Woburn  Station. 

25.  Lawes,   J.    B.    Journ.   Roy.   Agr.   Soc.    of   Engl.   Vol.   10. 

Rothamsted  Station. 

26.  Lawes,  J.   B.  Ibid. 

27.  Lawes,  J.   B.    Journ.    Roy.  Agr.  Soc.  of  Engl.  Vol.  12. 

Rothamsted  Station. 

28.  Lawes,   J.    B.    Journ.    Roy.    Agr.    Soc.   of   Engl.   Vol.    13.    1852,     From 

Rothamsted  Station. 

29.  Lawes,  J.   B.    Journ.  Roy.  Agr.  Soc.  of  Engl.     Vol.   16.     1855.      From 

Rothamsted  Station. 

30.  Shaw,  T.  Minn.  Agr,  Exp.  Sta,  Bui,  76.    1902. 

31.  Shaw,  T.  Ibid. 

32.  Watson,  G.  C.  and  Risser,  A.  K.  Penn.  Agr.  Exp.  Sta.  Bui.  57.     1901. 

33.  Carmichael,   B.   E.  Ohio  Agr.   Exp.  Sta.   Bui.   193.    1908. 

34.  Sheppard,  J.  H.  and  Richards,  W.  B.  No.  Dak.  Agr.  Exp.  Sta.  Bui.  73. 

1906. 

35.  Mairs,  T.  I.  and  Risser,  A.  K.  Penn.  Agr.  Exp.  Sta.  Bui.  64. 

36.  Mairs,  T.   I.  and   Risser,  A.   K.  Penn.  Agr.  Exp.  Sta.  Bui.   68. 

37.  Mairs,  T.  I.  and  Miller,  N.  G.  Penn.  Agr.  Exp.  Sta.  Bui.  74.     1905. 

38.  Mairs,  T.  I.  Penn.  Agr,  Exp.  Sta.  Bui  83.     1907. 

39.  Mairs,  T.   I.  Ibid. 

40.  Mairs,  T.   I.  Ibid. 

41.  Mairs,  T.  I.  and  Tomhave,  W.   H.  Penn.  Agr.  Exp.  Sta.  Bui.  88.     1908. 

42.  Mairs,  T.  I.  and   Tomhave,   W.    H.   Ibid. 

43.  Mumford,   H.   W.  111.   Agr.  Exp.  Sta.   Bui.   103.    1905. 

44.  Georgeson,  C.  C,  Burtis,  F.  C,  and  Shelton,  Wm,  Kan.  Agr.  Exp.   Sta. 

Bui.  34,    1895, 


From 


1849.     From 


1851.      From 


1903. 
1904. 


jp/j]  Uncertainty  in  Interpretation  of  Feeding  Experiments  579 

45.  Georgeson,  C.   C,   Burtis,    F.   C,   and   Otis,    D.    H.   Kan.  Agr.  Exp.   Sta. 

Bui.  39.    1893. 

46.  Georgeson,  C.   C,   Burtis,   F.  C,   and  Otis,   D.   H.  Kan.  Agr.   Exp.   Sta, 

Bui.    47.     1894. 

47.  Georgeson,  C.  C,   Burtis,   F.  C,  and  Otis,  D.   H.  Kan.  Agr.   Exp.    Sta. 

Bui.   51.    1895. 

48.  Robertson,  R.  Canadian  Experimental  Farms.  Report  for  1901.    360-363. 

49.  Voelcker,  J,  A.  Journ.   Roy.  Agr.  Soc.  of  Engl.  Vol,  63.    1902.     From 

Woburn  Station, 

50.  Voelcker,  J.  A,  Journ.  Roy.  Agr,   Soc.  of  Engl.  Vol,  62,    1901.     From 

Woburn  Station, 

51.  Voelcker,  J.  A.  Journ.  Roy,  Agr,   Soc.  of  Engl,  Vol,  60,    1899.     From 

Woburn  Station, 
'52.     Voelcker,  J.  A,  Journ.  Roy.  Agr.  Soc.  of  Engl.  Vol.  59.    1898.     From 
Woburn  Station, 

53.  Voelcker,  J,  A,  Ibid. 

54.  Voelcker,  J.  A,   Journ.  Roy.  Agr.  Soc.  of  Engl.  Vol.  56.    1895.     From 

Woburn  Station. 

55.  Voelcker,  J,  A.  Journ.  Roy.  Agr.  Soc,  of  Engl,  Vol.  57.    1896,     From 

Woburn  Station. 

56.  Voelcker,  J.   A.  Journ.  Roy,  Agr,  Soc.  of  Engl,  Vol.   53.    1892,     From 

Woburn  Station. 

57.  Voelcker,  J.  A.  Ibid, 

58.  Carlyle,  W.   L.  Wis.  Agr.  Exp.   Sta.   15th  Annual  Report.    1898. 

59.  Henry,  W.   A.  Wis.  Agr.  Exp.  Sta.  16th  Annual  Report,    1899. 

60.  Carlyle,  W,   L,  Ibid. 

61.  Michael,  L.  G.  and  Kennedy,  W,  J,  Iowa  Agr.  Exp.  Sta.  Bui.  113.  1910. 

62.  Wing,  H,  H,  N.  Y.  (Cornell)   Agr.  Exp.  Sta.  Bui.  220.     1904. 

63.  Henry,   W,   A.  Wis.   Agr.   Exp.   Sta.   15th  Annual   Report.    1898. 

64.  Kennedy,  W.  J.  and  Robbins,  E.  T.    Iowa  Agr.  Exp.  Sta.  Bui.  91.    1907. 

65.  Kennedy,    W,   J.  and    Robbins,    E.  T,   Ibid. 

66.  Henry,  W,   A,  Wis.  Agr.  Exp.  Sta.  17th  Annual  Report.    1900. 

67.  Henry,  W,  A,   Wis.  Agr.  Exp.   Sta.  15th  Annual  Report.    1898. 

68.  Henry,   W,   A,  Ibid. 

69.  Carlyle,   W.    L,   and   Hopkins,  A.   G.   Wis,   Agr,   Exp.   Sta.   17th   Annual 

Report.    1900. 

70.  Henry,  W,  A,  and  Otis  D.  H,  Wis.  Agr.  Exp.  Sta.  Bui.  145.    1907. 

71.  Henry,    W.   A.   and   Otis,    D.    H.   Ibid. 

72.  Henry,   W.  A.  and   Otis,   D.    H.  Ibid. 

73.  Sheppard,  J.  H.  and  Richards,  W.  B.  N.  Dak.  Agr,  Exp,  Sta.   Bui.    84. 

1909. 

74.  Georgeson,  C,  C,  Burtis,  F.  C,  and  Otis,  D,  H,  Kan.  Agr.  Exp.  Sta.  Bui, 

47.      1894. 

75.  Grisdale,  J.  H,  Canadian  Experimental  Farms.     Report  for  1899:  61. 

76.  Robertson,   R.   Canadian  Experimental  Farms.  Report  for  1900:  309-310, 

77.  Robertson,  R,  Canadian  Experimental  Farms.  Report  for  1899:  255-256. 

78.  Shutt,   F.  T.  Canadian  Experimental  Farms.     Report  for  1902:  219-222. 

79.  Shutt,   F.  T.  Canadian  Experimental  Farms.     Report  for  1902:  222-223. 

80.  Shutt,    F.  T.  Canadian  Experimental  Farms.     Report  for  1902:  226-227. 

81.  Shutt,   F.  T.  Canadian  Experimental  Farms.     Report  for  1902:    226-227. 

82.  Shutt,   F.  T,   Canadian  Experimental  Farms.     Report  for  1902:  228-230, 

83.  Gilbert,   A.  G,  Canadian  Experimental   Farms.    Report  for  1905:  256. 

84.  Shutt,  F.  T.  Canadian  Experimental  Farms.     Report  for  1898:  214, 


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J       I 


UNIVERSITY  OF  ILLINOIS-URBANA 


Q  630.7IL6B 
BULLETIN  UBBANA 
1651913 


C008 


iiiiiiiniini 


3  0112  019529764 


